%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU244+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:58:40 AM UTC 2026
% Result : Theorem 77.36s 77.68s
% Output : Proof 77.45s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(antisymmetry_r2_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
=> ~ proper_subset(B,A) ),
file('theBenchmark.p',antisymmetry_r2_xboole_0) ).
fof(cc1_funct_1,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('theBenchmark.p',cc1_funct_1) ).
fof(cc1_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc1_ordinal1) ).
fof(cc1_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('theBenchmark.p',cc1_relat_1) ).
fof(cc2_funct_1,axiom,
! [A] :
( ( function(A)
& empty(A)
& relation(A) )
=> ( one_to_one(A)
& function(A)
& relation(A) ) ),
file('theBenchmark.p',cc2_funct_1) ).
fof(cc2_ordinal1,axiom,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
=> ordinal(A) ),
file('theBenchmark.p',cc2_ordinal1) ).
fof(cc3_ordinal1,axiom,
! [A] :
( empty(A)
=> ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc3_ordinal1) ).
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(connectedness_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(B,A)
| ordinal_subset(A,B) ) ),
file('theBenchmark.p',connectedness_r1_ordinal1) ).
fof(d10_relat_1,axiom,
! [A,B] :
( relation(B)
=> ( B = identity_relation(A)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> ( C = D
& in(C,A) ) ) ) ),
file('theBenchmark.p',d10_relat_1) ).
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
fof(d11_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( relation(C)
=> ( C = relation_dom_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),A)
& in(D,B) ) ) ) ) ),
file('theBenchmark.p',d11_relat_1) ).
fof(d12_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( C = relation_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( D = apply(A,E)
& in(E,B)
& in(E,relation_dom(A)) ) ) ) ),
file('theBenchmark.p',d12_funct_1) ).
fof(d12_relat_1,axiom,
! [A,B] :
( relation(B)
=> ! [C] :
( relation(C)
=> ( C = relation_rng_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),B)
& in(E,A) ) ) ) ) ),
file('theBenchmark.p',d12_relat_1) ).
fof(d12_relat_2,axiom,
! [A] :
( relation(A)
=> ( antisymmetric(A)
<=> is_antisymmetric_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d12_relat_2) ).
fof(d13_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(apply(A,D),B)
& in(D,relation_dom(A)) ) ) ) ),
file('theBenchmark.p',d13_funct_1) ).
fof(d13_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = relation_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) ) ) ) ),
file('theBenchmark.p',d13_relat_1) ).
fof(d14_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) ) ) ) ),
file('theBenchmark.p',d14_relat_1) ).
fof(d14_relat_2,axiom,
! [A] :
( relation(A)
=> ( connected(A)
<=> is_connected_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d14_relat_2) ).
fof(d16_relat_2,axiom,
! [A] :
( relation(A)
=> ( transitive(A)
<=> is_transitive_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d16_relat_2) ).
fof(d1_enumset1,axiom,
! [A,B,C,D] :
( D = unordered_triple(A,B,C)
<=> ! [E] :
( in(E,D)
<=> ~ ( E != C
& E != B
& E != A ) ) ),
file('theBenchmark.p',d1_enumset1) ).
fof(d1_ordinal1,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('theBenchmark.p',d1_ordinal1) ).
fof(d1_relat_1,axiom,
! [A] :
( relation(A)
<=> ! [B] :
~ ( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) ) ),
file('theBenchmark.p',d1_relat_1) ).
fof(d1_relat_2,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_reflexive_in(A,B)
<=> ! [C] :
( in(C,B)
=> in(ordered_pair(C,C),A) ) ) ),
file('theBenchmark.p',d1_relat_2) ).
fof(d1_setfam_1,axiom,
! [A,B] :
( ( A = empty_set
=> ( B = set_meet(A)
<=> B = empty_set ) )
& ( A != empty_set
=> ( B = set_meet(A)
<=> ! [C] :
( in(C,B)
<=> ! [D] :
( in(D,A)
=> in(C,D) ) ) ) ) ),
file('theBenchmark.p',d1_setfam_1) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
fof(d1_zfmisc_1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('theBenchmark.p',d1_zfmisc_1) ).
fof(d2_ordinal1,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('theBenchmark.p',d2_ordinal1) ).
fof(d2_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( A = B
<=> ! [C,D] :
( in(ordered_pair(C,D),A)
<=> in(ordered_pair(C,D),B) ) ) ) ),
file('theBenchmark.p',d2_relat_1) ).
fof(d2_subset_1,axiom,
! [A,B] :
( ( empty(A)
=> ( element(B,A)
<=> empty(B) ) )
& ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) ) ),
file('theBenchmark.p',d2_subset_1) ).
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('theBenchmark.p',d2_tarski) ).
fof(d2_wellord1,axiom,
! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> ! [B] :
~ ( ! [C] :
~ ( disjoint(fiber(A,C),B)
& in(C,B) )
& B != empty_set
& subset(B,relation_field(A)) ) ) ),
file('theBenchmark.p',d2_wellord1) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('theBenchmark.p',d2_xboole_0) ).
fof(d2_zfmisc_1,axiom,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) ) ) ),
file('theBenchmark.p',d2_zfmisc_1) ).
fof(d3_ordinal1,axiom,
! [A] :
( epsilon_connected(A)
<=> ! [B,C] :
~ ( ~ in(C,B)
& B != C
& ~ in(B,C)
& in(C,A)
& in(B,A) ) ),
file('theBenchmark.p',d3_ordinal1) ).
fof(d3_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(A,B)
<=> ! [C,D] :
( in(ordered_pair(C,D),A)
=> in(ordered_pair(C,D),B) ) ) ) ),
file('theBenchmark.p',d3_relat_1) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(d3_wellord1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_well_founded_in(A,B)
<=> ! [C] :
~ ( ! [D] :
~ ( disjoint(fiber(A,D),C)
& in(D,C) )
& C != empty_set
& subset(C,B) ) ) ),
file('theBenchmark.p',d3_wellord1) ).
fof(d3_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d3_xboole_0) ).
fof(d4_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( ( ~ in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> C = empty_set ) )
& ( in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) ) ) ) ),
file('theBenchmark.p',d4_funct_1) ).
fof(d4_ordinal1,axiom,
! [A] :
( ordinal(A)
<=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',d4_ordinal1) ).
fof(d4_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('theBenchmark.p',d4_relat_1) ).
fof(d4_relat_2,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_antisymmetric_in(A,B)
<=> ! [C,D] :
( ( in(ordered_pair(D,C),A)
& in(ordered_pair(C,D),A)
& in(D,B)
& in(C,B) )
=> C = D ) ) ),
file('theBenchmark.p',d4_relat_2) ).
fof(d4_subset_1,axiom,
! [A] : cast_to_subset(A) = A,
file('theBenchmark.p',d4_subset_1) ).
fof(d4_tarski,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(D,A)
& in(C,D) ) ) ),
file('theBenchmark.p',d4_tarski) ).
fof(d4_wellord1,axiom,
! [A] :
( relation(A)
=> ( well_ordering(A)
<=> ( well_founded_relation(A)
& connected(A)
& antisymmetric(A)
& transitive(A)
& reflexive(A) ) ) ),
file('theBenchmark.p',d4_wellord1) ).
fof(d4_xboole_0,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d4_xboole_0) ).
fof(d5_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) ) ) ),
file('theBenchmark.p',d5_funct_1) ).
fof(d5_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('theBenchmark.p',d5_relat_1) ).
fof(d5_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,B) = set_difference(A,B) ),
file('theBenchmark.p',d5_subset_1) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(d5_wellord1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( well_orders(A,B)
<=> ( is_well_founded_in(A,B)
& is_connected_in(A,B)
& is_antisymmetric_in(A,B)
& is_transitive_in(A,B)
& is_reflexive_in(A,B) ) ) ),
file('theBenchmark.p',d5_wellord1) ).
fof(d6_ordinal1,axiom,
! [A] :
( being_limit_ordinal(A)
<=> A = union(A) ),
file('theBenchmark.p',d6_ordinal1) ).
fof(d6_relat_1,axiom,
! [A] :
( relation(A)
=> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
file('theBenchmark.p',d6_relat_1) ).
fof(d6_relat_2,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_connected_in(A,B)
<=> ! [C,D] :
~ ( ~ in(ordered_pair(D,C),A)
& ~ in(ordered_pair(C,D),A)
& C != D
& in(D,B)
& in(C,B) ) ) ),
file('theBenchmark.p',d6_relat_2) ).
fof(d7_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( B = relation_inverse(A)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> in(ordered_pair(D,C),A) ) ) ) ),
file('theBenchmark.p',d7_relat_1) ).
fof(d7_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('theBenchmark.p',d7_xboole_0) ).
fof(d8_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
<=> ! [B,C] :
( ( apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
=> B = C ) ) ),
file('theBenchmark.p',d8_funct_1) ).
fof(d8_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( relation(C)
=> ( C = relation_composition(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) ) ) ) ) ) ),
file('theBenchmark.p',d8_relat_1) ).
fof(d8_relat_2,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_transitive_in(A,B)
<=> ! [C,D,E] :
( ( in(ordered_pair(D,E),A)
& in(ordered_pair(C,D),A)
& in(E,B)
& in(D,B)
& in(C,B) )
=> in(ordered_pair(C,E),A) ) ) ),
file('theBenchmark.p',d8_relat_2) ).
fof(d8_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ! [C] :
( element(C,powerset(powerset(A)))
=> ( C = complements_of_subsets(A,B)
<=> ! [D] :
( element(D,powerset(A))
=> ( in(D,C)
<=> in(subset_complement(A,D),B) ) ) ) ) ),
file('theBenchmark.p',d8_setfam_1) ).
fof(d8_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('theBenchmark.p',d8_xboole_0) ).
fof(d9_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> function_inverse(A) = relation_inverse(A) ) ),
file('theBenchmark.p',d9_funct_1) ).
fof(d9_relat_2,axiom,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> is_reflexive_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d9_relat_2) ).
fof(dt_k10_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k10_relat_1) ).
fof(dt_k1_enumset1,axiom,
$true,
file('theBenchmark.p',dt_k1_enumset1) ).
fof(dt_k1_funct_1,axiom,
$true,
file('theBenchmark.p',dt_k1_funct_1) ).
fof(dt_k1_ordinal1,axiom,
$true,
file('theBenchmark.p',dt_k1_ordinal1) ).
fof(dt_k1_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k1_relat_1) ).
fof(dt_k1_setfam_1,axiom,
$true,
file('theBenchmark.p',dt_k1_setfam_1) ).
fof(dt_k1_tarski,axiom,
$true,
file('theBenchmark.p',dt_k1_tarski) ).
fof(dt_k1_wellord1,axiom,
$true,
file('theBenchmark.p',dt_k1_wellord1) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(dt_k2_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( function(function_inverse(A))
& relation(function_inverse(A)) ) ),
file('theBenchmark.p',dt_k2_funct_1) ).
fof(dt_k2_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k2_relat_1) ).
fof(dt_k2_subset_1,axiom,
! [A] : element(cast_to_subset(A),powerset(A)),
file('theBenchmark.p',dt_k2_subset_1) ).
fof(dt_k2_tarski,axiom,
$true,
file('theBenchmark.p',dt_k2_tarski) ).
fof(dt_k2_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k2_xboole_0) ).
fof(dt_k2_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k2_zfmisc_1) ).
fof(dt_k3_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k3_relat_1) ).
fof(dt_k3_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> element(subset_complement(A,B),powerset(A)) ),
file('theBenchmark.p',dt_k3_subset_1) ).
fof(dt_k3_tarski,axiom,
$true,
file('theBenchmark.p',dt_k3_tarski) ).
fof(dt_k3_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k3_xboole_0) ).
fof(dt_k4_relat_1,axiom,
! [A] :
( relation(A)
=> relation(relation_inverse(A)) ),
file('theBenchmark.p',dt_k4_relat_1) ).
fof(dt_k4_tarski,axiom,
$true,
file('theBenchmark.p',dt_k4_tarski) ).
fof(dt_k4_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k4_xboole_0) ).
fof(dt_k5_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(relation_composition(A,B)) ),
file('theBenchmark.p',dt_k5_relat_1) ).
fof(dt_k5_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(union_of_subsets(A,B),powerset(A)) ),
file('theBenchmark.p',dt_k5_setfam_1) ).
fof(dt_k6_relat_1,axiom,
! [A] : relation(identity_relation(A)),
file('theBenchmark.p',dt_k6_relat_1) ).
fof(dt_k6_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(meet_of_subsets(A,B),powerset(A)) ),
file('theBenchmark.p',dt_k6_setfam_1) ).
fof(dt_k6_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> element(subset_difference(A,B,C),powerset(A)) ),
file('theBenchmark.p',dt_k6_subset_1) ).
fof(dt_k7_relat_1,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('theBenchmark.p',dt_k7_relat_1) ).
fof(dt_k7_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(complements_of_subsets(A,B),powerset(powerset(A))) ),
file('theBenchmark.p',dt_k7_setfam_1) ).
fof(dt_k8_relat_1,axiom,
! [A,B] :
( relation(B)
=> relation(relation_rng_restriction(A,B)) ),
file('theBenchmark.p',dt_k8_relat_1) ).
fof(dt_k9_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k9_relat_1) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc10_relat_1,axiom,
! [A,B] :
( ( relation(B)
& empty(A) )
=> ( relation(relation_composition(B,A))
& empty(relation_composition(B,A)) ) ),
file('theBenchmark.p',fc10_relat_1) ).
fof(fc11_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_inverse(A))
& empty(relation_inverse(A)) ) ),
file('theBenchmark.p',fc11_relat_1) ).
fof(fc12_relat_1,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc12_relat_1) ).
fof(fc13_relat_1,axiom,
! [A,B] :
( ( relation_empty_yielding(A)
& relation(A) )
=> ( relation_empty_yielding(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) ) ),
file('theBenchmark.p',fc13_relat_1) ).
fof(fc1_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B)
& function(A)
& relation(A) )
=> ( function(relation_composition(A,B))
& relation(relation_composition(A,B)) ) ),
file('theBenchmark.p',fc1_funct_1) ).
fof(fc1_ordinal1,axiom,
! [A] : ~ empty(succ(A)),
file('theBenchmark.p',fc1_ordinal1) ).
fof(fc1_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(set_intersection2(A,B)) ),
file('theBenchmark.p',fc1_relat_1) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc1_zfmisc_1,axiom,
! [A,B] : ~ empty(ordered_pair(A,B)),
file('theBenchmark.p',fc1_zfmisc_1) ).
fof(fc2_funct_1,axiom,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
file('theBenchmark.p',fc2_funct_1) ).
fof(fc2_ordinal1,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('theBenchmark.p',fc2_ordinal1) ).
fof(fc2_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(set_union2(A,B)) ),
file('theBenchmark.p',fc2_relat_1) ).
fof(fc2_subset_1,axiom,
! [A] : ~ empty(singleton(A)),
file('theBenchmark.p',fc2_subset_1) ).
fof(fc2_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(A,B)) ),
file('theBenchmark.p',fc2_xboole_0) ).
fof(fc3_funct_1,axiom,
! [A] :
( ( one_to_one(A)
& function(A)
& relation(A) )
=> ( function(relation_inverse(A))
& relation(relation_inverse(A)) ) ),
file('theBenchmark.p',fc3_funct_1) ).
fof(fc3_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) ) ),
file('theBenchmark.p',fc3_ordinal1) ).
fof(fc3_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(set_difference(A,B)) ),
file('theBenchmark.p',fc3_relat_1) ).
fof(fc3_subset_1,axiom,
! [A,B] : ~ empty(unordered_pair(A,B)),
file('theBenchmark.p',fc3_subset_1) ).
fof(fc3_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(B,A)) ),
file('theBenchmark.p',fc3_xboole_0) ).
fof(fc4_funct_1,axiom,
! [A,B] :
( ( function(A)
& relation(A) )
=> ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) ) ),
file('theBenchmark.p',fc4_funct_1) ).
fof(fc4_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( ordinal(union(A))
& epsilon_connected(union(A))
& epsilon_transitive(union(A)) ) ),
file('theBenchmark.p',fc4_ordinal1) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(fc4_subset_1,axiom,
! [A,B] :
( ( ~ empty(B)
& ~ empty(A) )
=> ~ empty(cartesian_product2(A,B)) ),
file('theBenchmark.p',fc4_subset_1) ).
fof(fc5_relat_1,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_dom(A)) ),
file('theBenchmark.p',fc5_relat_1) ).
fof(fc6_relat_1,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_rng(A)) ),
file('theBenchmark.p',fc6_relat_1) ).
fof(fc7_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_dom(A))
& empty(relation_dom(A)) ) ),
file('theBenchmark.p',fc7_relat_1) ).
fof(fc8_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_rng(A))
& empty(relation_rng(A)) ) ),
file('theBenchmark.p',fc8_relat_1) ).
fof(fc9_relat_1,axiom,
! [A,B] :
( ( relation(B)
& empty(A) )
=> ( relation(relation_composition(A,B))
& empty(relation_composition(A,B)) ) ),
file('theBenchmark.p',fc9_relat_1) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('theBenchmark.p',idempotence_k3_xboole_0) ).
fof(involutiveness_k3_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,subset_complement(A,B)) = B ),
file('theBenchmark.p',involutiveness_k3_subset_1) ).
fof(involutiveness_k4_relat_1,axiom,
! [A] :
( relation(A)
=> relation_inverse(relation_inverse(A)) = A ),
file('theBenchmark.p',involutiveness_k4_relat_1) ).
fof(involutiveness_k7_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> complements_of_subsets(A,complements_of_subsets(A,B)) = B ),
file('theBenchmark.p',involutiveness_k7_setfam_1) ).
fof(irreflexivity_r2_xboole_0,axiom,
! [A,B] : ~ proper_subset(A,A),
file('theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(l1_wellord1,lemma,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> ! [B] :
( in(B,relation_field(A))
=> in(ordered_pair(B,B),A) ) ) ),
file('theBenchmark.p',l1_wellord1) ).
fof(l1_zfmisc_1,lemma,
! [A] : singleton(A) != empty_set,
file('theBenchmark.p',l1_zfmisc_1) ).
fof(l23_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('theBenchmark.p',l23_zfmisc_1) ).
fof(l25_zfmisc_1,lemma,
! [A,B] :
~ ( in(A,B)
& disjoint(singleton(A),B) ),
file('theBenchmark.p',l25_zfmisc_1) ).
fof(l28_zfmisc_1,lemma,
! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
file('theBenchmark.p',l28_zfmisc_1) ).
fof(l2_wellord1,lemma,
! [A] :
( relation(A)
=> ( transitive(A)
<=> ! [B,C,D] :
( ( in(ordered_pair(C,D),A)
& in(ordered_pair(B,C),A) )
=> in(ordered_pair(B,D),A) ) ) ),
file('theBenchmark.p',l2_wellord1) ).
fof(l2_zfmisc_1,lemma,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('theBenchmark.p',l2_zfmisc_1) ).
fof(l32_xboole_1,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',l32_xboole_1) ).
fof(l3_subset_1,lemma,
! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( in(C,B)
=> in(C,A) ) ),
file('theBenchmark.p',l3_subset_1) ).
fof(l3_wellord1,lemma,
! [A] :
( relation(A)
=> ( antisymmetric(A)
<=> ! [B,C] :
( ( in(ordered_pair(C,B),A)
& in(ordered_pair(B,C),A) )
=> B = C ) ) ),
file('theBenchmark.p',l3_wellord1) ).
fof(l3_zfmisc_1,lemma,
! [A,B,C] :
( subset(A,B)
=> ( subset(A,set_difference(B,singleton(C)))
| in(C,A) ) ),
file('theBenchmark.p',l3_zfmisc_1) ).
fof(l4_wellord1,lemma,
! [A] :
( relation(A)
=> ( connected(A)
<=> ! [B,C] :
~ ( ~ in(ordered_pair(C,B),A)
& ~ in(ordered_pair(B,C),A)
& B != C
& in(C,relation_field(A))
& in(B,relation_field(A)) ) ) ),
file('theBenchmark.p',l4_wellord1) ).
fof(l4_zfmisc_1,lemma,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',l4_zfmisc_1) ).
fof(l50_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
file('theBenchmark.p',l50_zfmisc_1) ).
fof(l55_zfmisc_1,lemma,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('theBenchmark.p',l55_zfmisc_1) ).
fof(l71_subset_1,lemma,
! [A,B] :
( ! [C] :
( in(C,A)
=> in(C,B) )
=> element(A,powerset(B)) ),
file('theBenchmark.p',l71_subset_1) ).
fof(l82_funct_1,lemma,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
<=> ( in(B,A)
& in(B,relation_dom(C)) ) ) ),
file('theBenchmark.p',l82_funct_1) ).
fof(rc1_funct_1,axiom,
? [A] :
( function(A)
& relation(A) ),
file('theBenchmark.p',rc1_funct_1) ).
fof(rc1_ordinal1,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
file('theBenchmark.p',rc1_ordinal1) ).
fof(rc1_relat_1,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('theBenchmark.p',rc1_relat_1) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc1_subset_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_funct_1,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('theBenchmark.p',rc2_funct_1) ).
fof(rc2_ordinal1,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc2_ordinal1) ).
fof(rc2_relat_1,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('theBenchmark.p',rc2_relat_1) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(rc3_funct_1,axiom,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc3_funct_1) ).
fof(rc3_ordinal1,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('theBenchmark.p',rc3_ordinal1) ).
fof(rc3_relat_1,axiom,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc3_relat_1) ).
fof(rc4_funct_1,axiom,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc4_funct_1) ).
fof(redefinition_k5_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> union_of_subsets(A,B) = union(B) ),
file('theBenchmark.p',redefinition_k5_setfam_1) ).
fof(redefinition_k6_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> meet_of_subsets(A,B) = set_meet(B) ),
file('theBenchmark.p',redefinition_k6_setfam_1) ).
fof(redefinition_k6_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> subset_difference(A,B,C) = set_difference(B,C) ),
file('theBenchmark.p',redefinition_k6_subset_1) ).
fof(redefinition_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('theBenchmark.p',redefinition_r1_ordinal1) ).
fof(reflexivity_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ordinal_subset(A,A) ),
file('theBenchmark.p',reflexivity_r1_ordinal1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t106_zfmisc_1,lemma,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('theBenchmark.p',t106_zfmisc_1) ).
fof(t10_ordinal1,lemma,
! [A] : in(A,succ(A)),
file('theBenchmark.p',t10_ordinal1) ).
fof(t10_zfmisc_1,lemma,
! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
file('theBenchmark.p',t10_zfmisc_1) ).
fof(t115_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_rng(relation_rng_restriction(B,C)))
<=> ( in(A,relation_rng(C))
& in(A,B) ) ) ),
file('theBenchmark.p',t115_relat_1) ).
fof(t116_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),A) ),
file('theBenchmark.p',t116_relat_1) ).
fof(t117_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng_restriction(A,B),B) ),
file('theBenchmark.p',t117_relat_1) ).
fof(t118_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ),
file('theBenchmark.p',t118_relat_1) ).
fof(t118_zfmisc_1,lemma,
! [A,B,C] :
( subset(A,B)
=> ( subset(cartesian_product2(C,A),cartesian_product2(C,B))
& subset(cartesian_product2(A,C),cartesian_product2(B,C)) ) ),
file('theBenchmark.p',t118_zfmisc_1) ).
fof(t119_relat_1,lemma,
! [A,B] :
( relation(B)
=> relation_rng(relation_rng_restriction(A,B)) = set_intersection2(relation_rng(B),A) ),
file('theBenchmark.p',t119_relat_1) ).
fof(t119_zfmisc_1,lemma,
! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('theBenchmark.p',t119_zfmisc_1) ).
fof(t12_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
file('theBenchmark.p',t12_xboole_1) ).
fof(t136_zfmisc_1,lemma,
! [A] :
? [B] :
( ! [C] :
~ ( ~ in(C,B)
& ~ are_equipotent(C,B)
& subset(C,B) )
& ! [C] :
( in(C,B)
=> in(powerset(C),B) )
& ! [C,D] :
( ( subset(D,C)
& in(C,B) )
=> in(D,B) )
& in(A,B) ),
file('theBenchmark.p',t136_zfmisc_1) ).
fof(t140_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> relation_dom_restriction(relation_rng_restriction(A,C),B) = relation_rng_restriction(A,relation_dom_restriction(C,B)) ),
file('theBenchmark.p',t140_relat_1) ).
fof(t143_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_image(C,B))
<=> ? [D] :
( in(D,B)
& in(ordered_pair(D,A),C)
& in(D,relation_dom(C)) ) ) ),
file('theBenchmark.p',t143_relat_1) ).
fof(t144_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_image(B,A),relation_rng(B)) ),
file('theBenchmark.p',t144_relat_1) ).
fof(t145_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> subset(relation_image(B,relation_inverse_image(B,A)),A) ),
file('theBenchmark.p',t145_funct_1) ).
fof(t145_relat_1,lemma,
! [A,B] :
( relation(B)
=> relation_image(B,A) = relation_image(B,set_intersection2(relation_dom(B),A)) ),
file('theBenchmark.p',t145_relat_1) ).
fof(t146_funct_1,lemma,
! [A,B] :
( relation(B)
=> ( subset(A,relation_dom(B))
=> subset(A,relation_inverse_image(B,relation_image(B,A))) ) ),
file('theBenchmark.p',t146_funct_1) ).
fof(t146_relat_1,lemma,
! [A] :
( relation(A)
=> relation_image(A,relation_dom(A)) = relation_rng(A) ),
file('theBenchmark.p',t146_relat_1) ).
fof(t147_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( subset(A,relation_rng(B))
=> relation_image(B,relation_inverse_image(B,A)) = A ) ),
file('theBenchmark.p',t147_funct_1) ).
fof(t160_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> relation_rng(relation_composition(A,B)) = relation_image(B,relation_rng(A)) ) ),
file('theBenchmark.p',t160_relat_1) ).
fof(t166_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_inverse_image(C,B))
<=> ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) ) ) ),
file('theBenchmark.p',t166_relat_1) ).
fof(t167_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_inverse_image(B,A),relation_dom(B)) ),
file('theBenchmark.p',t167_relat_1) ).
fof(t174_relat_1,lemma,
! [A,B] :
( relation(B)
=> ~ ( relation_inverse_image(B,A) = empty_set
& subset(A,relation_rng(B))
& A != empty_set ) ),
file('theBenchmark.p',t174_relat_1) ).
fof(t178_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( subset(A,B)
=> subset(relation_inverse_image(C,A),relation_inverse_image(C,B)) ) ),
file('theBenchmark.p',t178_relat_1) ).
fof(t17_xboole_1,lemma,
! [A,B] : subset(set_intersection2(A,B),A),
file('theBenchmark.p',t17_xboole_1) ).
fof(t19_xboole_1,lemma,
! [A,B,C] :
( ( subset(A,C)
& subset(A,B) )
=> subset(A,set_intersection2(B,C)) ),
file('theBenchmark.p',t19_xboole_1) ).
fof(t1_boole,axiom,
! [A] : set_union2(A,empty_set) = A,
file('theBenchmark.p',t1_boole) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t1_xboole_1,lemma,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('theBenchmark.p',t1_xboole_1) ).
fof(t1_zfmisc_1,lemma,
powerset(empty_set) = singleton(empty_set),
file('theBenchmark.p',t1_zfmisc_1) ).
fof(t20_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_rng(C))
& in(A,relation_dom(C)) ) ) ),
file('theBenchmark.p',t20_relat_1) ).
fof(t21_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(relation_composition(C,B)))
<=> ( in(apply(C,A),relation_dom(B))
& in(A,relation_dom(C)) ) ) ) ),
file('theBenchmark.p',t21_funct_1) ).
fof(t21_ordinal1,lemma,
! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ( proper_subset(A,B)
=> in(A,B) ) ) ),
file('theBenchmark.p',t21_ordinal1) ).
fof(t21_relat_1,lemma,
! [A] :
( relation(A)
=> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))) ),
file('theBenchmark.p',t21_relat_1) ).
fof(t22_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(relation_composition(C,B)))
=> apply(relation_composition(C,B),A) = apply(B,apply(C,A)) ) ) ),
file('theBenchmark.p',t22_funct_1) ).
fof(t23_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(B))
=> apply(relation_composition(B,C),A) = apply(C,apply(B,A)) ) ) ),
file('theBenchmark.p',t23_funct_1) ).
fof(t23_ordinal1,lemma,
! [A,B] :
( ordinal(B)
=> ( in(A,B)
=> ordinal(A) ) ),
file('theBenchmark.p',t23_ordinal1) ).
fof(t24_ordinal1,lemma,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ in(B,A)
& A != B
& ~ in(A,B) ) ) ),
file('theBenchmark.p',t24_ordinal1) ).
fof(t25_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(A,B)
=> ( subset(relation_rng(A),relation_rng(B))
& subset(relation_dom(A),relation_dom(B)) ) ) ) ),
file('theBenchmark.p',t25_relat_1) ).
fof(t26_xboole_1,lemma,
! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ),
file('theBenchmark.p',t26_xboole_1) ).
fof(t28_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('theBenchmark.p',t28_xboole_1) ).
fof(t2_boole,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
file('theBenchmark.p',t2_boole) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('theBenchmark.p',t2_tarski) ).
fof(t2_xboole_1,lemma,
! [A] : subset(empty_set,A),
file('theBenchmark.p',t2_xboole_1) ).
fof(t30_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_field(C))
& in(A,relation_field(C)) ) ) ),
file('theBenchmark.p',t30_relat_1) ).
fof(t31_ordinal1,lemma,
! [A] :
( ! [B] :
( in(B,A)
=> ( subset(B,A)
& ordinal(B) ) )
=> ordinal(A) ),
file('theBenchmark.p',t31_ordinal1) ).
fof(t32_ordinal1,lemma,
! [A,B] :
( ordinal(B)
=> ~ ( ! [C] :
( ordinal(C)
=> ~ ( ! [D] :
( ordinal(D)
=> ( in(D,A)
=> ordinal_subset(C,D) ) )
& in(C,A) ) )
& A != empty_set
& subset(A,B) ) ),
file('theBenchmark.p',t32_ordinal1) ).
fof(t33_ordinal1,lemma,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(A,B)
<=> ordinal_subset(succ(A),B) ) ) ),
file('theBenchmark.p',t33_ordinal1) ).
fof(t33_xboole_1,lemma,
! [A,B,C] :
( subset(A,B)
=> subset(set_difference(A,C),set_difference(B,C)) ),
file('theBenchmark.p',t33_xboole_1) ).
fof(t33_zfmisc_1,lemma,
! [A,B,C,D] :
( ordered_pair(A,B) = ordered_pair(C,D)
=> ( B = D
& A = C ) ),
file('theBenchmark.p',t33_zfmisc_1) ).
fof(t34_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( B = identity_relation(A)
<=> ( ! [C] :
( in(C,A)
=> apply(B,C) = C )
& relation_dom(B) = A ) ) ),
file('theBenchmark.p',t34_funct_1) ).
fof(t35_funct_1,lemma,
! [A,B] :
( in(B,A)
=> apply(identity_relation(A),B) = B ),
file('theBenchmark.p',t35_funct_1) ).
fof(t36_xboole_1,lemma,
! [A,B] : subset(set_difference(A,B),A),
file('theBenchmark.p',t36_xboole_1) ).
fof(t37_relat_1,lemma,
! [A] :
( relation(A)
=> ( relation_dom(A) = relation_rng(relation_inverse(A))
& relation_rng(A) = relation_dom(relation_inverse(A)) ) ),
file('theBenchmark.p',t37_relat_1) ).
fof(t37_xboole_1,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',t37_xboole_1) ).
fof(t37_zfmisc_1,lemma,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('theBenchmark.p',t37_zfmisc_1) ).
fof(t38_zfmisc_1,lemma,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(B,C)
& in(A,C) ) ),
file('theBenchmark.p',t38_zfmisc_1) ).
fof(t39_xboole_1,lemma,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
file('theBenchmark.p',t39_xboole_1) ).
fof(t39_zfmisc_1,lemma,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',t39_zfmisc_1) ).
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
file('theBenchmark.p',t3_boole) ).
fof(t3_ordinal1,lemma,
! [A,B,C] :
~ ( in(C,A)
& in(B,C)
& in(A,B) ),
file('theBenchmark.p',t3_ordinal1) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t3_xboole_0,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t3_xboole_0) ).
fof(t3_xboole_1,lemma,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('theBenchmark.p',t3_xboole_1) ).
fof(t40_xboole_1,lemma,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
file('theBenchmark.p',t40_xboole_1) ).
fof(t41_ordinal1,lemma,
! [A] :
( ordinal(A)
=> ( being_limit_ordinal(A)
<=> ! [B] :
( ordinal(B)
=> ( in(B,A)
=> in(succ(B),A) ) ) ) ),
file('theBenchmark.p',t41_ordinal1) ).
fof(t42_ordinal1,lemma,
! [A] :
( ordinal(A)
=> ( ~ ( being_limit_ordinal(A)
& ? [B] :
( A = succ(B)
& ordinal(B) ) )
& ~ ( ! [B] :
( ordinal(B)
=> A != succ(B) )
& ~ being_limit_ordinal(A) ) ) ),
file('theBenchmark.p',t42_ordinal1) ).
fof(t43_subset_1,lemma,
! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,powerset(A))
=> ( disjoint(B,C)
<=> subset(B,subset_complement(A,C)) ) ) ),
file('theBenchmark.p',t43_subset_1) ).
fof(t44_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> subset(relation_dom(relation_composition(A,B)),relation_dom(A)) ) ),
file('theBenchmark.p',t44_relat_1) ).
fof(t45_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> subset(relation_rng(relation_composition(A,B)),relation_rng(B)) ) ),
file('theBenchmark.p',t45_relat_1) ).
fof(t45_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> B = set_union2(A,set_difference(B,A)) ),
file('theBenchmark.p',t45_xboole_1) ).
fof(t46_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(relation_rng(A),relation_dom(B))
=> relation_dom(relation_composition(A,B)) = relation_dom(A) ) ) ),
file('theBenchmark.p',t46_relat_1) ).
fof(t46_setfam_1,lemma,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ~ ( complements_of_subsets(A,B) = empty_set
& B != empty_set ) ),
file('theBenchmark.p',t46_setfam_1) ).
fof(t46_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('theBenchmark.p',t46_zfmisc_1) ).
fof(t47_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(relation_dom(A),relation_rng(B))
=> relation_rng(relation_composition(B,A)) = relation_rng(A) ) ) ),
file('theBenchmark.p',t47_relat_1) ).
fof(t47_setfam_1,lemma,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> subset_difference(A,cast_to_subset(A),union_of_subsets(A,B)) = meet_of_subsets(A,complements_of_subsets(A,B)) ) ),
file('theBenchmark.p',t47_setfam_1) ).
fof(t48_setfam_1,lemma,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> union_of_subsets(A,complements_of_subsets(A,B)) = subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B)) ) ),
file('theBenchmark.p',t48_setfam_1) ).
fof(t48_xboole_1,lemma,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
file('theBenchmark.p',t48_xboole_1) ).
fof(t4_boole,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
file('theBenchmark.p',t4_boole) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t4_xboole_0,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t4_xboole_0) ).
fof(t50_subset_1,lemma,
! [A] :
( A != empty_set
=> ! [B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,A)
=> ( ~ in(C,B)
=> in(C,subset_complement(A,B)) ) ) ) ),
file('theBenchmark.p',t50_subset_1) ).
fof(t54_funct_1,lemma,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( B = function_inverse(A)
<=> ( ! [C,D] :
( ( ( C = apply(A,D)
& in(D,relation_dom(A)) )
=> ( D = apply(B,C)
& in(C,relation_rng(A)) ) )
& ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
=> ( C = apply(A,D)
& in(D,relation_dom(A)) ) ) )
& relation_dom(B) = relation_rng(A) ) ) ) ) ),
file('theBenchmark.p',t54_funct_1) ).
fof(t54_subset_1,lemma,
! [A,B,C] :
( element(C,powerset(A))
=> ~ ( in(B,C)
& in(B,subset_complement(A,C)) ) ),
file('theBenchmark.p',t54_subset_1) ).
fof(t55_funct_1,lemma,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_dom(A) = relation_rng(function_inverse(A))
& relation_rng(A) = relation_dom(function_inverse(A)) ) ) ),
file('theBenchmark.p',t55_funct_1) ).
fof(t56_relat_1,lemma,
! [A] :
( relation(A)
=> ( ! [B,C] : ~ in(ordered_pair(B,C),A)
=> A = empty_set ) ),
file('theBenchmark.p',t56_relat_1) ).
fof(t57_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( ( in(A,relation_rng(B))
& one_to_one(B) )
=> ( A = apply(relation_composition(function_inverse(B),B),A)
& A = apply(B,apply(function_inverse(B),A)) ) ) ),
file('theBenchmark.p',t57_funct_1) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t5_wellord1,lemma,
! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> is_well_founded_in(A,relation_field(A)) ) ),
file('theBenchmark.p',t5_wellord1) ).
fof(t60_relat_1,lemma,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('theBenchmark.p',t60_relat_1) ).
fof(t60_xboole_1,lemma,
! [A,B] :
~ ( proper_subset(B,A)
& subset(A,B) ),
file('theBenchmark.p',t60_xboole_1) ).
fof(t62_funct_1,lemma,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> one_to_one(function_inverse(A)) ) ),
file('theBenchmark.p',t62_funct_1) ).
fof(t63_xboole_1,lemma,
! [A,B,C] :
( ( disjoint(B,C)
& subset(A,B) )
=> disjoint(A,C) ),
file('theBenchmark.p',t63_xboole_1) ).
fof(t64_relat_1,lemma,
! [A] :
( relation(A)
=> ( ( relation_rng(A) = empty_set
| relation_dom(A) = empty_set )
=> A = empty_set ) ),
file('theBenchmark.p',t64_relat_1) ).
fof(t65_relat_1,lemma,
! [A] :
( relation(A)
=> ( relation_dom(A) = empty_set
<=> relation_rng(A) = empty_set ) ),
file('theBenchmark.p',t65_relat_1) ).
fof(t65_zfmisc_1,lemma,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('theBenchmark.p',t65_zfmisc_1) ).
fof(t68_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( B = relation_dom_restriction(C,A)
<=> ( ! [D] :
( in(D,relation_dom(B))
=> apply(B,D) = apply(C,D) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) ) ) ) ),
file('theBenchmark.p',t68_funct_1) ).
fof(t69_enumset1,lemma,
! [A] : unordered_pair(A,A) = singleton(A),
file('theBenchmark.p',t69_enumset1) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t6_zfmisc_1,lemma,
! [A,B] :
( subset(singleton(A),singleton(B))
=> A = B ),
file('theBenchmark.p',t6_zfmisc_1) ).
fof(t70_funct_1,lemma,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
file('theBenchmark.p',t70_funct_1) ).
fof(t71_relat_1,lemma,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
file('theBenchmark.p',t71_relat_1) ).
fof(t72_funct_1,lemma,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,A)
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
file('theBenchmark.p',t72_funct_1) ).
fof(t74_relat_1,lemma,
! [A,B,C,D] :
( relation(D)
=> ( in(ordered_pair(A,B),relation_composition(identity_relation(C),D))
<=> ( in(ordered_pair(A,B),D)
& in(A,C) ) ) ),
file('theBenchmark.p',t74_relat_1) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t7_tarski,axiom,
! [A,B] :
~ ( ! [C] :
~ ( ! [D] :
~ ( in(D,C)
& in(D,B) )
& in(C,B) )
& in(A,B) ),
file('theBenchmark.p',t7_tarski) ).
fof(t7_xboole_1,lemma,
! [A,B] : subset(A,set_union2(A,B)),
file('theBenchmark.p',t7_xboole_1) ).
fof(t83_xboole_1,lemma,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('theBenchmark.p',t83_xboole_1) ).
fof(t86_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_dom(relation_dom_restriction(C,B)))
<=> ( in(A,relation_dom(C))
& in(A,B) ) ) ),
file('theBenchmark.p',t86_relat_1) ).
fof(t88_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_dom_restriction(B,A),B) ),
file('theBenchmark.p',t88_relat_1) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(t8_funct_1,lemma,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(ordered_pair(A,B),C)
<=> ( B = apply(C,A)
& in(A,relation_dom(C)) ) ) ),
file('theBenchmark.p',t8_funct_1) ).
fof(t8_wellord1,conjecture,
! [A] :
( relation(A)
=> ( well_orders(A,relation_field(A))
<=> well_ordering(A) ) ),
file('theBenchmark.p',t8_wellord1) ).
fof(t8_xboole_1,lemma,
! [A,B,C] :
( ( subset(C,B)
& subset(A,B) )
=> subset(set_union2(A,C),B) ),
file('theBenchmark.p',t8_xboole_1) ).
fof(t8_zfmisc_1,lemma,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ),
file('theBenchmark.p',t8_zfmisc_1) ).
fof(t90_relat_1,lemma,
! [A,B] :
( relation(B)
=> relation_dom(relation_dom_restriction(B,A)) = set_intersection2(relation_dom(B),A) ),
file('theBenchmark.p',t90_relat_1) ).
fof(t92_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
file('theBenchmark.p',t92_zfmisc_1) ).
fof(t94_relat_1,lemma,
! [A,B] :
( relation(B)
=> relation_dom_restriction(B,A) = relation_composition(identity_relation(A),B) ),
file('theBenchmark.p',t94_relat_1) ).
fof(t99_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B)) ),
file('theBenchmark.p',t99_relat_1) ).
fof(t99_zfmisc_1,lemma,
! [A] : union(powerset(A)) = A,
file('theBenchmark.p',t99_zfmisc_1) ).
fof(t9_tarski,axiom,
! [A] :
? [B] :
( ! [C] :
~ ( ~ in(C,B)
& ~ are_equipotent(C,B)
& subset(C,B) )
& ! [C] :
~ ( ! [D] :
~ ( ! [E] :
( subset(E,C)
=> in(E,D) )
& in(D,B) )
& in(C,B) )
& ! [C,D] :
( ( subset(D,C)
& in(C,B) )
=> in(D,B) )
& in(A,B) ),
file('theBenchmark.p',t9_tarski) ).
fof(t9_zfmisc_1,lemma,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> B = C ),
file('theBenchmark.p',t9_zfmisc_1) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ proper_subset(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(f_2_2,plain,
! [U_3,U_2] :
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_3_2,plain,
! [U_4] :
( function(U_4)
| ~ empty(U_4) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( function(U_4)
| ~ empty(U_4) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[cc1_ordinal1]) ).
fof(f_4_2,plain,
! [U_5] :
( ( epsilon_connected(U_5)
& epsilon_transitive(U_5) )
| ~ ordinal(U_5) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( epsilon_transitive(U_5)
| ~ ordinal(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( epsilon_connected(U_5)
| ~ ordinal(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_5_2,plain,
! [U_6] :
( relation(U_6)
| ~ empty(U_6) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( relation(U_6)
| ~ empty(U_6) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A] :
( ( one_to_one(A)
& function(A)
& relation(A) )
| ~ function(A)
| ~ empty(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[cc2_funct_1]) ).
fof(f_6_2,plain,
! [U_7] :
( ( one_to_one(U_7)
& function(U_7)
& relation(U_7) )
| ~ function(U_7)
| ~ empty(U_7)
| ~ relation(U_7) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( relation(U_7)
| ~ function(U_7)
| ~ empty(U_7)
| ~ relation(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( function(U_7)
| ~ function(U_7)
| ~ empty(U_7)
| ~ relation(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_5,plain,
( one_to_one(U_7)
| ~ function(U_7)
| ~ empty(U_7)
| ~ relation(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A] :
( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[cc2_ordinal1]) ).
fof(f_7_2,plain,
! [U_8] :
( ordinal(U_8)
| ~ epsilon_connected(U_8)
| ~ epsilon_transitive(U_8) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( ordinal(U_8)
| ~ epsilon_connected(U_8)
| ~ epsilon_transitive(U_8) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [A] :
( ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc3_ordinal1]) ).
fof(f_8_2,plain,
! [U_9] :
( ( ordinal(U_9)
& epsilon_connected(U_9)
& epsilon_transitive(U_9) )
| ~ empty(U_9) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( epsilon_transitive(U_9)
| ~ empty(U_9) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( epsilon_connected(U_9)
| ~ empty(U_9) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_5,plain,
( ordinal(U_9)
| ~ empty(U_9) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_9_2,plain,
! [U_11,U_10] : unordered_pair(U_11,U_10) = unordered_pair(U_10,U_11),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
unordered_pair(U_11,U_10) = unordered_pair(U_10,U_11),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_10_2,plain,
! [U_13,U_12] : set_union2(U_13,U_12) = set_union2(U_12,U_13),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
set_union2(U_13,U_12) = set_union2(U_12,U_13),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_11_2,plain,
! [U_15,U_14] : set_intersection2(U_15,U_14) = set_intersection2(U_14,U_15),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
set_intersection2(U_15,U_14) = set_intersection2(U_14,U_15),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A,B] :
( ordinal_subset(B,A)
| ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[connectedness_r1_ordinal1]) ).
fof(f_12_2,plain,
! [U_17,U_16] :
( ordinal_subset(U_16,U_17)
| ordinal_subset(U_17,U_16)
| ~ ordinal(U_16)
| ~ ordinal(U_17) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( ordinal_subset(U_16,U_17)
| ordinal_subset(U_17,U_16)
| ~ ordinal(U_16)
| ~ ordinal(U_17) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [A,B] :
( ( ( B = identity_relation(A)
| ? [C,D] :
( ( ~ in(ordered_pair(C,D),B)
& C = D
& in(C,A) )
| ( ( C != D
| ~ in(C,A) )
& in(ordered_pair(C,D),B) ) ) )
& ( ! [C,D] :
( ( in(ordered_pair(C,D),B)
| C != D
| ~ in(C,A) )
& ( ( C = D
& in(C,A) )
| ~ in(ordered_pair(C,D),B) ) )
| B != identity_relation(A) ) )
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[d10_relat_1]) ).
fof(f_13_2,plain,
! [U_23,U_22] :
( ( ( U_22 = identity_relation(U_23)
| ? [U_21,U_20] :
( ( ~ in(ordered_pair(U_21,U_20),U_22)
& U_21 = U_20
& in(U_21,U_23) )
| ( ( U_21 != U_20
| ~ in(U_21,U_23) )
& in(ordered_pair(U_21,U_20),U_22) ) ) )
& ( ! [U_19,U_18] :
( ( in(ordered_pair(U_19,U_18),U_22)
| U_19 != U_18
| ~ in(U_19,U_23) )
& ( ( U_19 = U_18
& in(U_19,U_23) )
| ~ in(ordered_pair(U_19,U_18),U_22) ) )
| U_22 != identity_relation(U_23) ) )
| ~ relation(U_22) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_23,U_22] :
( ( ( U_22 = identity_relation(U_23)
| ? [U_31,U_29] :
( ~ in(ordered_pair(U_31,U_29),U_22)
& U_31 = U_29
& in(U_31,U_23) )
| ? [U_30,U_28] :
( ( U_30 != U_28
| ~ in(U_30,U_23) )
& in(ordered_pair(U_30,U_28),U_22) ) )
& ( ( ! [U_27,U_25] :
( in(ordered_pair(U_27,U_25),U_22)
| U_27 != U_25
| ~ in(U_27,U_23) )
& ! [U_26,U_24] :
( ( U_26 = U_24
& in(U_26,U_23) )
| ~ in(ordered_pair(U_26,U_24),U_22) ) )
| U_22 != identity_relation(U_23) ) )
| ~ relation(U_22) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
fof(f_13_4,plain,
! [U_23,U_22] :
( ( ( U_22 = identity_relation(U_23)
| ? [U_31,U_29] :
( ~ in(ordered_pair(U_31,U_29),U_22)
& U_31 = U_29
& in(U_31,U_23) )
| ? [U_28] :
( ( sK1(U_23,U_22) != U_28
| ~ in(sK1(U_23,U_22),U_23) )
& in(ordered_pair(sK1(U_23,U_22),U_28),U_22) ) )
& ( ( ! [U_27,U_25] :
( in(ordered_pair(U_27,U_25),U_22)
| U_27 != U_25
| ~ in(U_27,U_23) )
& ! [U_26,U_24] :
( ( U_26 = U_24
& in(U_26,U_23) )
| ~ in(ordered_pair(U_26,U_24),U_22) ) )
| U_22 != identity_relation(U_23) ) )
| ~ relation(U_22) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_30,sK1(U_23,U_22))],[f_13_3]) ).
fof(f_13_5,plain,
! [U_23,U_22] :
( ( ( U_22 = identity_relation(U_23)
| ? [U_31,U_29] :
( ~ in(ordered_pair(U_31,U_29),U_22)
& U_31 = U_29
& in(U_31,U_23) )
| ( ( sK1(U_23,U_22) != sK2(U_23,U_22)
| ~ in(sK1(U_23,U_22),U_23) )
& in(ordered_pair(sK1(U_23,U_22),sK2(U_23,U_22)),U_22) ) )
& ( ( ! [U_27,U_25] :
( in(ordered_pair(U_27,U_25),U_22)
| U_27 != U_25
| ~ in(U_27,U_23) )
& ! [U_26,U_24] :
( ( U_26 = U_24
& in(U_26,U_23) )
| ~ in(ordered_pair(U_26,U_24),U_22) ) )
| U_22 != identity_relation(U_23) ) )
| ~ relation(U_22) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_28,sK2(U_23,U_22))],[f_13_4]) ).
fof(f_13_6,plain,
! [U_23,U_22] :
( ( ( U_22 = identity_relation(U_23)
| ? [U_29] :
( ~ in(ordered_pair(sK3(U_23,U_22),U_29),U_22)
& sK3(U_23,U_22) = U_29
& in(sK3(U_23,U_22),U_23) )
| ( ( sK1(U_23,U_22) != sK2(U_23,U_22)
| ~ in(sK1(U_23,U_22),U_23) )
& in(ordered_pair(sK1(U_23,U_22),sK2(U_23,U_22)),U_22) ) )
& ( ( ! [U_27,U_25] :
( in(ordered_pair(U_27,U_25),U_22)
| U_27 != U_25
| ~ in(U_27,U_23) )
& ! [U_26,U_24] :
( ( U_26 = U_24
& in(U_26,U_23) )
| ~ in(ordered_pair(U_26,U_24),U_22) ) )
| U_22 != identity_relation(U_23) ) )
| ~ relation(U_22) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_31,sK3(U_23,U_22))],[f_13_5]) ).
fof(f_13_7,plain,
! [U_23,U_22] :
( ( ( U_22 = identity_relation(U_23)
| ( ~ in(ordered_pair(sK3(U_23,U_22),sK4(U_23,U_22)),U_22)
& sK3(U_23,U_22) = sK4(U_23,U_22)
& in(sK3(U_23,U_22),U_23) )
| ( ( sK1(U_23,U_22) != sK2(U_23,U_22)
| ~ in(sK1(U_23,U_22),U_23) )
& in(ordered_pair(sK1(U_23,U_22),sK2(U_23,U_22)),U_22) ) )
& ( ( ! [U_27,U_25] :
( in(ordered_pair(U_27,U_25),U_22)
| U_27 != U_25
| ~ in(U_27,U_23) )
& ! [U_26,U_24] :
( ( U_26 = U_24
& in(U_26,U_23) )
| ~ in(ordered_pair(U_26,U_24),U_22) ) )
| U_22 != identity_relation(U_23) ) )
| ~ relation(U_22) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_29,sK4(U_23,U_22))],[f_13_6]) ).
cnf(f_13_8,plain,
( in(U_26,U_23)
| ~ in(ordered_pair(U_26,U_24),U_22)
| U_22 != identity_relation(U_23)
| ~ relation(U_22) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_9,plain,
( U_26 = U_24
| ~ in(ordered_pair(U_26,U_24),U_22)
| U_22 != identity_relation(U_23)
| ~ relation(U_22) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_10,plain,
( in(ordered_pair(U_27,U_25),U_22)
| U_27 != U_25
| ~ in(U_27,U_23)
| U_22 != identity_relation(U_23)
| ~ relation(U_22) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_11,plain,
( in(sK3(U_23,U_22),U_23)
| in(ordered_pair(sK1(U_23,U_22),sK2(U_23,U_22)),U_22)
| U_22 = identity_relation(U_23)
| ~ relation(U_22) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_12,plain,
( sK3(U_23,U_22) = sK4(U_23,U_22)
| in(ordered_pair(sK1(U_23,U_22),sK2(U_23,U_22)),U_22)
| U_22 = identity_relation(U_23)
| ~ relation(U_22) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_13,plain,
( ~ in(ordered_pair(sK3(U_23,U_22),sK4(U_23,U_22)),U_22)
| in(ordered_pair(sK1(U_23,U_22),sK2(U_23,U_22)),U_22)
| U_22 = identity_relation(U_23)
| ~ relation(U_22) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_14,plain,
( in(sK3(U_23,U_22),U_23)
| sK1(U_23,U_22) != sK2(U_23,U_22)
| ~ in(sK1(U_23,U_22),U_23)
| U_22 = identity_relation(U_23)
| ~ relation(U_22) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_15,plain,
( sK3(U_23,U_22) = sK4(U_23,U_22)
| sK1(U_23,U_22) != sK2(U_23,U_22)
| ~ in(sK1(U_23,U_22),U_23)
| U_22 = identity_relation(U_23)
| ~ relation(U_22) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_16,plain,
( ~ in(ordered_pair(sK3(U_23,U_22),sK4(U_23,U_22)),U_22)
| sK1(U_23,U_22) != sK2(U_23,U_22)
| ~ in(sK1(U_23,U_22),U_23)
| U_22 = identity_relation(U_23)
| ~ relation(U_22) ),
inference(clausify,[status(thm)],[f_13_7]) ).
fof(f_14_1,plain,
! [A,B] :
( ( A = B
| ~ subset(B,A)
| ~ subset(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(fof_nnf,[status(thm)],[d10_xboole_0]) ).
fof(f_14_2,plain,
! [U_33,U_32] :
( ( U_33 = U_32
| ~ subset(U_32,U_33)
| ~ subset(U_33,U_32) )
& ( ( subset(U_32,U_33)
& subset(U_33,U_32) )
| U_33 != U_32 ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_37,U_35] :
( U_37 = U_35
| ~ subset(U_35,U_37)
| ~ subset(U_37,U_35) )
& ! [U_36,U_34] :
( ( subset(U_34,U_36)
& subset(U_36,U_34) )
| U_36 != U_34 ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( subset(U_36,U_34)
| U_36 != U_34 ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_5,plain,
( subset(U_34,U_36)
| U_36 != U_34 ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_6,plain,
( U_37 = U_35
| ~ subset(U_35,U_37)
| ~ subset(U_37,U_35) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [A] :
( ! [B,C] :
( ( ( C = relation_dom_restriction(A,B)
| ? [D,E] :
( ( ~ in(ordered_pair(D,E),C)
& in(ordered_pair(D,E),A)
& in(D,B) )
| ( ( ~ in(ordered_pair(D,E),A)
| ~ in(D,B) )
& in(ordered_pair(D,E),C) ) ) )
& ( ! [D,E] :
( ( in(ordered_pair(D,E),C)
| ~ in(ordered_pair(D,E),A)
| ~ in(D,B) )
& ( ( in(ordered_pair(D,E),A)
& in(D,B) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_dom_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d11_relat_1]) ).
fof(f_15_2,plain,
! [U_44] :
( ! [U_43,U_42] :
( ( ( U_42 = relation_dom_restriction(U_44,U_43)
| ? [U_41,U_40] :
( ( ~ in(ordered_pair(U_41,U_40),U_42)
& in(ordered_pair(U_41,U_40),U_44)
& in(U_41,U_43) )
| ( ( ~ in(ordered_pair(U_41,U_40),U_44)
| ~ in(U_41,U_43) )
& in(ordered_pair(U_41,U_40),U_42) ) ) )
& ( ! [U_39,U_38] :
( ( in(ordered_pair(U_39,U_38),U_42)
| ~ in(ordered_pair(U_39,U_38),U_44)
| ~ in(U_39,U_43) )
& ( ( in(ordered_pair(U_39,U_38),U_44)
& in(U_39,U_43) )
| ~ in(ordered_pair(U_39,U_38),U_42) ) )
| U_42 != relation_dom_restriction(U_44,U_43) ) )
| ~ relation(U_42) )
| ~ relation(U_44) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_44] :
( ! [U_43,U_42] :
( ( ( U_42 = relation_dom_restriction(U_44,U_43)
| ? [U_52,U_50] :
( ~ in(ordered_pair(U_52,U_50),U_42)
& in(ordered_pair(U_52,U_50),U_44)
& in(U_52,U_43) )
| ? [U_51,U_49] :
( ( ~ in(ordered_pair(U_51,U_49),U_44)
| ~ in(U_51,U_43) )
& in(ordered_pair(U_51,U_49),U_42) ) )
& ( ( ! [U_48,U_46] :
( in(ordered_pair(U_48,U_46),U_42)
| ~ in(ordered_pair(U_48,U_46),U_44)
| ~ in(U_48,U_43) )
& ! [U_47,U_45] :
( ( in(ordered_pair(U_47,U_45),U_44)
& in(U_47,U_43) )
| ~ in(ordered_pair(U_47,U_45),U_42) ) )
| U_42 != relation_dom_restriction(U_44,U_43) ) )
| ~ relation(U_42) )
| ~ relation(U_44) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
fof(f_15_4,plain,
! [U_44] :
( ! [U_43,U_42] :
( ( ( U_42 = relation_dom_restriction(U_44,U_43)
| ? [U_52,U_50] :
( ~ in(ordered_pair(U_52,U_50),U_42)
& in(ordered_pair(U_52,U_50),U_44)
& in(U_52,U_43) )
| ? [U_49] :
( ( ~ in(ordered_pair(sK5(U_44,U_43,U_42),U_49),U_44)
| ~ in(sK5(U_44,U_43,U_42),U_43) )
& in(ordered_pair(sK5(U_44,U_43,U_42),U_49),U_42) ) )
& ( ( ! [U_48,U_46] :
( in(ordered_pair(U_48,U_46),U_42)
| ~ in(ordered_pair(U_48,U_46),U_44)
| ~ in(U_48,U_43) )
& ! [U_47,U_45] :
( ( in(ordered_pair(U_47,U_45),U_44)
& in(U_47,U_43) )
| ~ in(ordered_pair(U_47,U_45),U_42) ) )
| U_42 != relation_dom_restriction(U_44,U_43) ) )
| ~ relation(U_42) )
| ~ relation(U_44) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_51,sK5(U_44,U_43,U_42))],[f_15_3]) ).
fof(f_15_5,plain,
! [U_44] :
( ! [U_43,U_42] :
( ( ( U_42 = relation_dom_restriction(U_44,U_43)
| ? [U_52,U_50] :
( ~ in(ordered_pair(U_52,U_50),U_42)
& in(ordered_pair(U_52,U_50),U_44)
& in(U_52,U_43) )
| ( ( ~ in(ordered_pair(sK5(U_44,U_43,U_42),sK6(U_44,U_43,U_42)),U_44)
| ~ in(sK5(U_44,U_43,U_42),U_43) )
& in(ordered_pair(sK5(U_44,U_43,U_42),sK6(U_44,U_43,U_42)),U_42) ) )
& ( ( ! [U_48,U_46] :
( in(ordered_pair(U_48,U_46),U_42)
| ~ in(ordered_pair(U_48,U_46),U_44)
| ~ in(U_48,U_43) )
& ! [U_47,U_45] :
( ( in(ordered_pair(U_47,U_45),U_44)
& in(U_47,U_43) )
| ~ in(ordered_pair(U_47,U_45),U_42) ) )
| U_42 != relation_dom_restriction(U_44,U_43) ) )
| ~ relation(U_42) )
| ~ relation(U_44) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_49,sK6(U_44,U_43,U_42))],[f_15_4]) ).
fof(f_15_6,plain,
! [U_44] :
( ! [U_43,U_42] :
( ( ( U_42 = relation_dom_restriction(U_44,U_43)
| ? [U_50] :
( ~ in(ordered_pair(sK7(U_44,U_43,U_42),U_50),U_42)
& in(ordered_pair(sK7(U_44,U_43,U_42),U_50),U_44)
& in(sK7(U_44,U_43,U_42),U_43) )
| ( ( ~ in(ordered_pair(sK5(U_44,U_43,U_42),sK6(U_44,U_43,U_42)),U_44)
| ~ in(sK5(U_44,U_43,U_42),U_43) )
& in(ordered_pair(sK5(U_44,U_43,U_42),sK6(U_44,U_43,U_42)),U_42) ) )
& ( ( ! [U_48,U_46] :
( in(ordered_pair(U_48,U_46),U_42)
| ~ in(ordered_pair(U_48,U_46),U_44)
| ~ in(U_48,U_43) )
& ! [U_47,U_45] :
( ( in(ordered_pair(U_47,U_45),U_44)
& in(U_47,U_43) )
| ~ in(ordered_pair(U_47,U_45),U_42) ) )
| U_42 != relation_dom_restriction(U_44,U_43) ) )
| ~ relation(U_42) )
| ~ relation(U_44) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_52,sK7(U_44,U_43,U_42))],[f_15_5]) ).
fof(f_15_7,plain,
! [U_44] :
( ! [U_43,U_42] :
( ( ( U_42 = relation_dom_restriction(U_44,U_43)
| ( ~ in(ordered_pair(sK7(U_44,U_43,U_42),sK8(U_44,U_43,U_42)),U_42)
& in(ordered_pair(sK7(U_44,U_43,U_42),sK8(U_44,U_43,U_42)),U_44)
& in(sK7(U_44,U_43,U_42),U_43) )
| ( ( ~ in(ordered_pair(sK5(U_44,U_43,U_42),sK6(U_44,U_43,U_42)),U_44)
| ~ in(sK5(U_44,U_43,U_42),U_43) )
& in(ordered_pair(sK5(U_44,U_43,U_42),sK6(U_44,U_43,U_42)),U_42) ) )
& ( ( ! [U_48,U_46] :
( in(ordered_pair(U_48,U_46),U_42)
| ~ in(ordered_pair(U_48,U_46),U_44)
| ~ in(U_48,U_43) )
& ! [U_47,U_45] :
( ( in(ordered_pair(U_47,U_45),U_44)
& in(U_47,U_43) )
| ~ in(ordered_pair(U_47,U_45),U_42) ) )
| U_42 != relation_dom_restriction(U_44,U_43) ) )
| ~ relation(U_42) )
| ~ relation(U_44) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_50,sK8(U_44,U_43,U_42))],[f_15_6]) ).
cnf(f_15_8,plain,
( in(U_47,U_43)
| ~ in(ordered_pair(U_47,U_45),U_42)
| U_42 != relation_dom_restriction(U_44,U_43)
| ~ relation(U_42)
| ~ relation(U_44) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_9,plain,
( in(ordered_pair(U_47,U_45),U_44)
| ~ in(ordered_pair(U_47,U_45),U_42)
| U_42 != relation_dom_restriction(U_44,U_43)
| ~ relation(U_42)
| ~ relation(U_44) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_10,plain,
( in(ordered_pair(U_48,U_46),U_42)
| ~ in(ordered_pair(U_48,U_46),U_44)
| ~ in(U_48,U_43)
| U_42 != relation_dom_restriction(U_44,U_43)
| ~ relation(U_42)
| ~ relation(U_44) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_11,plain,
( in(sK7(U_44,U_43,U_42),U_43)
| in(ordered_pair(sK5(U_44,U_43,U_42),sK6(U_44,U_43,U_42)),U_42)
| U_42 = relation_dom_restriction(U_44,U_43)
| ~ relation(U_42)
| ~ relation(U_44) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_12,plain,
( in(ordered_pair(sK7(U_44,U_43,U_42),sK8(U_44,U_43,U_42)),U_44)
| in(ordered_pair(sK5(U_44,U_43,U_42),sK6(U_44,U_43,U_42)),U_42)
| U_42 = relation_dom_restriction(U_44,U_43)
| ~ relation(U_42)
| ~ relation(U_44) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_13,plain,
( ~ in(ordered_pair(sK7(U_44,U_43,U_42),sK8(U_44,U_43,U_42)),U_42)
| in(ordered_pair(sK5(U_44,U_43,U_42),sK6(U_44,U_43,U_42)),U_42)
| U_42 = relation_dom_restriction(U_44,U_43)
| ~ relation(U_42)
| ~ relation(U_44) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_14,plain,
( in(sK7(U_44,U_43,U_42),U_43)
| ~ in(ordered_pair(sK5(U_44,U_43,U_42),sK6(U_44,U_43,U_42)),U_44)
| ~ in(sK5(U_44,U_43,U_42),U_43)
| U_42 = relation_dom_restriction(U_44,U_43)
| ~ relation(U_42)
| ~ relation(U_44) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_15,plain,
( in(ordered_pair(sK7(U_44,U_43,U_42),sK8(U_44,U_43,U_42)),U_44)
| ~ in(ordered_pair(sK5(U_44,U_43,U_42),sK6(U_44,U_43,U_42)),U_44)
| ~ in(sK5(U_44,U_43,U_42),U_43)
| U_42 = relation_dom_restriction(U_44,U_43)
| ~ relation(U_42)
| ~ relation(U_44) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_16,plain,
( ~ in(ordered_pair(sK7(U_44,U_43,U_42),sK8(U_44,U_43,U_42)),U_42)
| ~ in(ordered_pair(sK5(U_44,U_43,U_42),sK6(U_44,U_43,U_42)),U_44)
| ~ in(sK5(U_44,U_43,U_42),U_43)
| U_42 = relation_dom_restriction(U_44,U_43)
| ~ relation(U_42)
| ~ relation(U_44) ),
inference(clausify,[status(thm)],[f_15_7]) ).
fof(f_16_1,plain,
! [A] :
( ! [B,C] :
( ( C = relation_image(A,B)
| ? [D] :
( ( ~ in(D,C)
& ? [E] :
( D = apply(A,E)
& in(E,B)
& in(E,relation_dom(A)) ) )
| ( ! [E] :
( D != apply(A,E)
| ~ in(E,B)
| ~ in(E,relation_dom(A)) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ! [E] :
( D != apply(A,E)
| ~ in(E,B)
| ~ in(E,relation_dom(A)) ) )
& ( ? [E] :
( D = apply(A,E)
& in(E,B)
& in(E,relation_dom(A)) )
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d12_funct_1]) ).
fof(f_16_2,plain,
! [U_61] :
( ! [U_60,U_59] :
( ( U_59 = relation_image(U_61,U_60)
| ? [U_58] :
( ( ~ in(U_58,U_59)
& ? [U_57] :
( U_58 = apply(U_61,U_57)
& in(U_57,U_60)
& in(U_57,relation_dom(U_61)) ) )
| ( ! [U_56] :
( U_58 != apply(U_61,U_56)
| ~ in(U_56,U_60)
| ~ in(U_56,relation_dom(U_61)) )
& in(U_58,U_59) ) ) )
& ( ! [U_55] :
( ( in(U_55,U_59)
| ! [U_54] :
( U_55 != apply(U_61,U_54)
| ~ in(U_54,U_60)
| ~ in(U_54,relation_dom(U_61)) ) )
& ( ? [U_53] :
( U_55 = apply(U_61,U_53)
& in(U_53,U_60)
& in(U_53,relation_dom(U_61)) )
| ~ in(U_55,U_59) ) )
| U_59 != relation_image(U_61,U_60) ) )
| ~ function(U_61)
| ~ relation(U_61) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_61] :
( ( ! [U_69,U_67] :
( U_67 = relation_image(U_61,U_69)
| ? [U_65] :
( ~ in(U_65,U_67)
& ? [U_57] :
( U_65 = apply(U_61,U_57)
& in(U_57,U_69)
& in(U_57,relation_dom(U_61)) ) )
| ? [U_64] :
( ! [U_56] :
( U_64 != apply(U_61,U_56)
| ~ in(U_56,U_69)
| ~ in(U_56,relation_dom(U_61)) )
& in(U_64,U_67) ) )
& ! [U_68,U_66] :
( ( ! [U_63] :
( in(U_63,U_66)
| ! [U_54] :
( U_63 != apply(U_61,U_54)
| ~ in(U_54,U_68)
| ~ in(U_54,relation_dom(U_61)) ) )
& ! [U_62] :
( ? [U_53] :
( U_62 = apply(U_61,U_53)
& in(U_53,U_68)
& in(U_53,relation_dom(U_61)) )
| ~ in(U_62,U_66) ) )
| U_66 != relation_image(U_61,U_68) ) )
| ~ function(U_61)
| ~ relation(U_61) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
fof(f_16_4,plain,
! [U_61] :
( ( ! [U_69,U_67] :
( U_67 = relation_image(U_61,U_69)
| ? [U_65] :
( ~ in(U_65,U_67)
& ? [U_57] :
( U_65 = apply(U_61,U_57)
& in(U_57,U_69)
& in(U_57,relation_dom(U_61)) ) )
| ? [U_64] :
( ! [U_56] :
( U_64 != apply(U_61,U_56)
| ~ in(U_56,U_69)
| ~ in(U_56,relation_dom(U_61)) )
& in(U_64,U_67) ) )
& ! [U_68,U_66] :
( ( ! [U_63] :
( in(U_63,U_66)
| ! [U_54] :
( U_63 != apply(U_61,U_54)
| ~ in(U_54,U_68)
| ~ in(U_54,relation_dom(U_61)) ) )
& ! [U_62] :
( ( U_62 = apply(U_61,sK9(U_61,U_68,U_66,U_62))
& in(sK9(U_61,U_68,U_66,U_62),U_68)
& in(sK9(U_61,U_68,U_66,U_62),relation_dom(U_61)) )
| ~ in(U_62,U_66) ) )
| U_66 != relation_image(U_61,U_68) ) )
| ~ function(U_61)
| ~ relation(U_61) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_53,sK9(U_61,U_68,U_66,U_62))],[f_16_3]) ).
fof(f_16_5,plain,
! [U_61] :
( ( ! [U_69,U_67] :
( U_67 = relation_image(U_61,U_69)
| ? [U_65] :
( ~ in(U_65,U_67)
& ? [U_57] :
( U_65 = apply(U_61,U_57)
& in(U_57,U_69)
& in(U_57,relation_dom(U_61)) ) )
| ( ! [U_56] :
( sK10(U_61,U_69,U_67) != apply(U_61,U_56)
| ~ in(U_56,U_69)
| ~ in(U_56,relation_dom(U_61)) )
& in(sK10(U_61,U_69,U_67),U_67) ) )
& ! [U_68,U_66] :
( ( ! [U_63] :
( in(U_63,U_66)
| ! [U_54] :
( U_63 != apply(U_61,U_54)
| ~ in(U_54,U_68)
| ~ in(U_54,relation_dom(U_61)) ) )
& ! [U_62] :
( ( U_62 = apply(U_61,sK9(U_61,U_68,U_66,U_62))
& in(sK9(U_61,U_68,U_66,U_62),U_68)
& in(sK9(U_61,U_68,U_66,U_62),relation_dom(U_61)) )
| ~ in(U_62,U_66) ) )
| U_66 != relation_image(U_61,U_68) ) )
| ~ function(U_61)
| ~ relation(U_61) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_64,sK10(U_61,U_69,U_67))],[f_16_4]) ).
fof(f_16_6,plain,
! [U_61] :
( ( ! [U_69,U_67] :
( U_67 = relation_image(U_61,U_69)
| ( ~ in(sK11(U_61,U_69,U_67),U_67)
& ? [U_57] :
( sK11(U_61,U_69,U_67) = apply(U_61,U_57)
& in(U_57,U_69)
& in(U_57,relation_dom(U_61)) ) )
| ( ! [U_56] :
( sK10(U_61,U_69,U_67) != apply(U_61,U_56)
| ~ in(U_56,U_69)
| ~ in(U_56,relation_dom(U_61)) )
& in(sK10(U_61,U_69,U_67),U_67) ) )
& ! [U_68,U_66] :
( ( ! [U_63] :
( in(U_63,U_66)
| ! [U_54] :
( U_63 != apply(U_61,U_54)
| ~ in(U_54,U_68)
| ~ in(U_54,relation_dom(U_61)) ) )
& ! [U_62] :
( ( U_62 = apply(U_61,sK9(U_61,U_68,U_66,U_62))
& in(sK9(U_61,U_68,U_66,U_62),U_68)
& in(sK9(U_61,U_68,U_66,U_62),relation_dom(U_61)) )
| ~ in(U_62,U_66) ) )
| U_66 != relation_image(U_61,U_68) ) )
| ~ function(U_61)
| ~ relation(U_61) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_65,sK11(U_61,U_69,U_67))],[f_16_5]) ).
fof(f_16_7,plain,
! [U_61] :
( ( ! [U_69,U_67] :
( U_67 = relation_image(U_61,U_69)
| ( ~ in(sK11(U_61,U_69,U_67),U_67)
& sK11(U_61,U_69,U_67) = apply(U_61,sK12(U_61,U_69,U_67))
& in(sK12(U_61,U_69,U_67),U_69)
& in(sK12(U_61,U_69,U_67),relation_dom(U_61)) )
| ( ! [U_56] :
( sK10(U_61,U_69,U_67) != apply(U_61,U_56)
| ~ in(U_56,U_69)
| ~ in(U_56,relation_dom(U_61)) )
& in(sK10(U_61,U_69,U_67),U_67) ) )
& ! [U_68,U_66] :
( ( ! [U_63] :
( in(U_63,U_66)
| ! [U_54] :
( U_63 != apply(U_61,U_54)
| ~ in(U_54,U_68)
| ~ in(U_54,relation_dom(U_61)) ) )
& ! [U_62] :
( ( U_62 = apply(U_61,sK9(U_61,U_68,U_66,U_62))
& in(sK9(U_61,U_68,U_66,U_62),U_68)
& in(sK9(U_61,U_68,U_66,U_62),relation_dom(U_61)) )
| ~ in(U_62,U_66) ) )
| U_66 != relation_image(U_61,U_68) ) )
| ~ function(U_61)
| ~ relation(U_61) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_57,sK12(U_61,U_69,U_67))],[f_16_6]) ).
cnf(f_16_8,plain,
( in(sK9(U_61,U_68,U_66,U_62),relation_dom(U_61))
| ~ in(U_62,U_66)
| U_66 != relation_image(U_61,U_68)
| ~ function(U_61)
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_9,plain,
( in(sK9(U_61,U_68,U_66,U_62),U_68)
| ~ in(U_62,U_66)
| U_66 != relation_image(U_61,U_68)
| ~ function(U_61)
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_10,plain,
( U_62 = apply(U_61,sK9(U_61,U_68,U_66,U_62))
| ~ in(U_62,U_66)
| U_66 != relation_image(U_61,U_68)
| ~ function(U_61)
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_11,plain,
( in(U_63,U_66)
| U_63 != apply(U_61,U_54)
| ~ in(U_54,U_68)
| ~ in(U_54,relation_dom(U_61))
| U_66 != relation_image(U_61,U_68)
| ~ function(U_61)
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_12,plain,
( in(sK12(U_61,U_69,U_67),relation_dom(U_61))
| in(sK10(U_61,U_69,U_67),U_67)
| U_67 = relation_image(U_61,U_69)
| ~ function(U_61)
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_13,plain,
( in(sK12(U_61,U_69,U_67),U_69)
| in(sK10(U_61,U_69,U_67),U_67)
| U_67 = relation_image(U_61,U_69)
| ~ function(U_61)
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_14,plain,
( sK11(U_61,U_69,U_67) = apply(U_61,sK12(U_61,U_69,U_67))
| in(sK10(U_61,U_69,U_67),U_67)
| U_67 = relation_image(U_61,U_69)
| ~ function(U_61)
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_15,plain,
( ~ in(sK11(U_61,U_69,U_67),U_67)
| in(sK10(U_61,U_69,U_67),U_67)
| U_67 = relation_image(U_61,U_69)
| ~ function(U_61)
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_16,plain,
( in(sK12(U_61,U_69,U_67),relation_dom(U_61))
| sK10(U_61,U_69,U_67) != apply(U_61,U_56)
| ~ in(U_56,U_69)
| ~ in(U_56,relation_dom(U_61))
| U_67 = relation_image(U_61,U_69)
| ~ function(U_61)
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_17,plain,
( in(sK12(U_61,U_69,U_67),U_69)
| sK10(U_61,U_69,U_67) != apply(U_61,U_56)
| ~ in(U_56,U_69)
| ~ in(U_56,relation_dom(U_61))
| U_67 = relation_image(U_61,U_69)
| ~ function(U_61)
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_18,plain,
( sK11(U_61,U_69,U_67) = apply(U_61,sK12(U_61,U_69,U_67))
| sK10(U_61,U_69,U_67) != apply(U_61,U_56)
| ~ in(U_56,U_69)
| ~ in(U_56,relation_dom(U_61))
| U_67 = relation_image(U_61,U_69)
| ~ function(U_61)
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_19,plain,
( ~ in(sK11(U_61,U_69,U_67),U_67)
| sK10(U_61,U_69,U_67) != apply(U_61,U_56)
| ~ in(U_56,U_69)
| ~ in(U_56,relation_dom(U_61))
| U_67 = relation_image(U_61,U_69)
| ~ function(U_61)
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_16_7]) ).
fof(f_17_1,plain,
! [A,B] :
( ! [C] :
( ( ( C = relation_rng_restriction(A,B)
| ? [D,E] :
( ( ~ in(ordered_pair(D,E),C)
& in(ordered_pair(D,E),B)
& in(E,A) )
| ( ( ~ in(ordered_pair(D,E),B)
| ~ in(E,A) )
& in(ordered_pair(D,E),C) ) ) )
& ( ! [D,E] :
( ( in(ordered_pair(D,E),C)
| ~ in(ordered_pair(D,E),B)
| ~ in(E,A) )
& ( ( in(ordered_pair(D,E),B)
& in(E,A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_rng_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[d12_relat_1]) ).
fof(f_17_2,plain,
! [U_76,U_75] :
( ! [U_74] :
( ( ( U_74 = relation_rng_restriction(U_76,U_75)
| ? [U_73,U_72] :
( ( ~ in(ordered_pair(U_73,U_72),U_74)
& in(ordered_pair(U_73,U_72),U_75)
& in(U_72,U_76) )
| ( ( ~ in(ordered_pair(U_73,U_72),U_75)
| ~ in(U_72,U_76) )
& in(ordered_pair(U_73,U_72),U_74) ) ) )
& ( ! [U_71,U_70] :
( ( in(ordered_pair(U_71,U_70),U_74)
| ~ in(ordered_pair(U_71,U_70),U_75)
| ~ in(U_70,U_76) )
& ( ( in(ordered_pair(U_71,U_70),U_75)
& in(U_70,U_76) )
| ~ in(ordered_pair(U_71,U_70),U_74) ) )
| U_74 != relation_rng_restriction(U_76,U_75) ) )
| ~ relation(U_74) )
| ~ relation(U_75) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_76,U_75] :
( ! [U_74] :
( ( ( U_74 = relation_rng_restriction(U_76,U_75)
| ? [U_84,U_82] :
( ~ in(ordered_pair(U_84,U_82),U_74)
& in(ordered_pair(U_84,U_82),U_75)
& in(U_82,U_76) )
| ? [U_83,U_81] :
( ( ~ in(ordered_pair(U_83,U_81),U_75)
| ~ in(U_81,U_76) )
& in(ordered_pair(U_83,U_81),U_74) ) )
& ( ( ! [U_80,U_78] :
( in(ordered_pair(U_80,U_78),U_74)
| ~ in(ordered_pair(U_80,U_78),U_75)
| ~ in(U_78,U_76) )
& ! [U_79,U_77] :
( ( in(ordered_pair(U_79,U_77),U_75)
& in(U_77,U_76) )
| ~ in(ordered_pair(U_79,U_77),U_74) ) )
| U_74 != relation_rng_restriction(U_76,U_75) ) )
| ~ relation(U_74) )
| ~ relation(U_75) ),
inference(miniscope,[status(thm)],[f_17_2]) ).
fof(f_17_4,plain,
! [U_76,U_75] :
( ! [U_74] :
( ( ( U_74 = relation_rng_restriction(U_76,U_75)
| ? [U_84,U_82] :
( ~ in(ordered_pair(U_84,U_82),U_74)
& in(ordered_pair(U_84,U_82),U_75)
& in(U_82,U_76) )
| ? [U_81] :
( ( ~ in(ordered_pair(sK13(U_76,U_75,U_74),U_81),U_75)
| ~ in(U_81,U_76) )
& in(ordered_pair(sK13(U_76,U_75,U_74),U_81),U_74) ) )
& ( ( ! [U_80,U_78] :
( in(ordered_pair(U_80,U_78),U_74)
| ~ in(ordered_pair(U_80,U_78),U_75)
| ~ in(U_78,U_76) )
& ! [U_79,U_77] :
( ( in(ordered_pair(U_79,U_77),U_75)
& in(U_77,U_76) )
| ~ in(ordered_pair(U_79,U_77),U_74) ) )
| U_74 != relation_rng_restriction(U_76,U_75) ) )
| ~ relation(U_74) )
| ~ relation(U_75) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_83,sK13(U_76,U_75,U_74))],[f_17_3]) ).
fof(f_17_5,plain,
! [U_76,U_75] :
( ! [U_74] :
( ( ( U_74 = relation_rng_restriction(U_76,U_75)
| ? [U_84,U_82] :
( ~ in(ordered_pair(U_84,U_82),U_74)
& in(ordered_pair(U_84,U_82),U_75)
& in(U_82,U_76) )
| ( ( ~ in(ordered_pair(sK13(U_76,U_75,U_74),sK14(U_76,U_75,U_74)),U_75)
| ~ in(sK14(U_76,U_75,U_74),U_76) )
& in(ordered_pair(sK13(U_76,U_75,U_74),sK14(U_76,U_75,U_74)),U_74) ) )
& ( ( ! [U_80,U_78] :
( in(ordered_pair(U_80,U_78),U_74)
| ~ in(ordered_pair(U_80,U_78),U_75)
| ~ in(U_78,U_76) )
& ! [U_79,U_77] :
( ( in(ordered_pair(U_79,U_77),U_75)
& in(U_77,U_76) )
| ~ in(ordered_pair(U_79,U_77),U_74) ) )
| U_74 != relation_rng_restriction(U_76,U_75) ) )
| ~ relation(U_74) )
| ~ relation(U_75) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_81,sK14(U_76,U_75,U_74))],[f_17_4]) ).
fof(f_17_6,plain,
! [U_76,U_75] :
( ! [U_74] :
( ( ( U_74 = relation_rng_restriction(U_76,U_75)
| ? [U_82] :
( ~ in(ordered_pair(sK15(U_76,U_75,U_74),U_82),U_74)
& in(ordered_pair(sK15(U_76,U_75,U_74),U_82),U_75)
& in(U_82,U_76) )
| ( ( ~ in(ordered_pair(sK13(U_76,U_75,U_74),sK14(U_76,U_75,U_74)),U_75)
| ~ in(sK14(U_76,U_75,U_74),U_76) )
& in(ordered_pair(sK13(U_76,U_75,U_74),sK14(U_76,U_75,U_74)),U_74) ) )
& ( ( ! [U_80,U_78] :
( in(ordered_pair(U_80,U_78),U_74)
| ~ in(ordered_pair(U_80,U_78),U_75)
| ~ in(U_78,U_76) )
& ! [U_79,U_77] :
( ( in(ordered_pair(U_79,U_77),U_75)
& in(U_77,U_76) )
| ~ in(ordered_pair(U_79,U_77),U_74) ) )
| U_74 != relation_rng_restriction(U_76,U_75) ) )
| ~ relation(U_74) )
| ~ relation(U_75) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_84,sK15(U_76,U_75,U_74))],[f_17_5]) ).
fof(f_17_7,plain,
! [U_76,U_75] :
( ! [U_74] :
( ( ( U_74 = relation_rng_restriction(U_76,U_75)
| ( ~ in(ordered_pair(sK15(U_76,U_75,U_74),sK16(U_76,U_75,U_74)),U_74)
& in(ordered_pair(sK15(U_76,U_75,U_74),sK16(U_76,U_75,U_74)),U_75)
& in(sK16(U_76,U_75,U_74),U_76) )
| ( ( ~ in(ordered_pair(sK13(U_76,U_75,U_74),sK14(U_76,U_75,U_74)),U_75)
| ~ in(sK14(U_76,U_75,U_74),U_76) )
& in(ordered_pair(sK13(U_76,U_75,U_74),sK14(U_76,U_75,U_74)),U_74) ) )
& ( ( ! [U_80,U_78] :
( in(ordered_pair(U_80,U_78),U_74)
| ~ in(ordered_pair(U_80,U_78),U_75)
| ~ in(U_78,U_76) )
& ! [U_79,U_77] :
( ( in(ordered_pair(U_79,U_77),U_75)
& in(U_77,U_76) )
| ~ in(ordered_pair(U_79,U_77),U_74) ) )
| U_74 != relation_rng_restriction(U_76,U_75) ) )
| ~ relation(U_74) )
| ~ relation(U_75) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_82,sK16(U_76,U_75,U_74))],[f_17_6]) ).
cnf(f_17_8,plain,
( in(U_77,U_76)
| ~ in(ordered_pair(U_79,U_77),U_74)
| U_74 != relation_rng_restriction(U_76,U_75)
| ~ relation(U_74)
| ~ relation(U_75) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_9,plain,
( in(ordered_pair(U_79,U_77),U_75)
| ~ in(ordered_pair(U_79,U_77),U_74)
| U_74 != relation_rng_restriction(U_76,U_75)
| ~ relation(U_74)
| ~ relation(U_75) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_10,plain,
( in(ordered_pair(U_80,U_78),U_74)
| ~ in(ordered_pair(U_80,U_78),U_75)
| ~ in(U_78,U_76)
| U_74 != relation_rng_restriction(U_76,U_75)
| ~ relation(U_74)
| ~ relation(U_75) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_11,plain,
( in(sK16(U_76,U_75,U_74),U_76)
| in(ordered_pair(sK13(U_76,U_75,U_74),sK14(U_76,U_75,U_74)),U_74)
| U_74 = relation_rng_restriction(U_76,U_75)
| ~ relation(U_74)
| ~ relation(U_75) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_12,plain,
( in(ordered_pair(sK15(U_76,U_75,U_74),sK16(U_76,U_75,U_74)),U_75)
| in(ordered_pair(sK13(U_76,U_75,U_74),sK14(U_76,U_75,U_74)),U_74)
| U_74 = relation_rng_restriction(U_76,U_75)
| ~ relation(U_74)
| ~ relation(U_75) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_13,plain,
( ~ in(ordered_pair(sK15(U_76,U_75,U_74),sK16(U_76,U_75,U_74)),U_74)
| in(ordered_pair(sK13(U_76,U_75,U_74),sK14(U_76,U_75,U_74)),U_74)
| U_74 = relation_rng_restriction(U_76,U_75)
| ~ relation(U_74)
| ~ relation(U_75) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_14,plain,
( in(sK16(U_76,U_75,U_74),U_76)
| ~ in(ordered_pair(sK13(U_76,U_75,U_74),sK14(U_76,U_75,U_74)),U_75)
| ~ in(sK14(U_76,U_75,U_74),U_76)
| U_74 = relation_rng_restriction(U_76,U_75)
| ~ relation(U_74)
| ~ relation(U_75) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_15,plain,
( in(ordered_pair(sK15(U_76,U_75,U_74),sK16(U_76,U_75,U_74)),U_75)
| ~ in(ordered_pair(sK13(U_76,U_75,U_74),sK14(U_76,U_75,U_74)),U_75)
| ~ in(sK14(U_76,U_75,U_74),U_76)
| U_74 = relation_rng_restriction(U_76,U_75)
| ~ relation(U_74)
| ~ relation(U_75) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_16,plain,
( ~ in(ordered_pair(sK15(U_76,U_75,U_74),sK16(U_76,U_75,U_74)),U_74)
| ~ in(ordered_pair(sK13(U_76,U_75,U_74),sK14(U_76,U_75,U_74)),U_75)
| ~ in(sK14(U_76,U_75,U_74),U_76)
| U_74 = relation_rng_restriction(U_76,U_75)
| ~ relation(U_74)
| ~ relation(U_75) ),
inference(clausify,[status(thm)],[f_17_7]) ).
fof(f_18_1,plain,
! [A] :
( ( ( antisymmetric(A)
| ~ is_antisymmetric_in(A,relation_field(A)) )
& ( is_antisymmetric_in(A,relation_field(A))
| ~ antisymmetric(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d12_relat_2]) ).
fof(f_18_2,plain,
! [U_85] :
( ( ( antisymmetric(U_85)
| ~ is_antisymmetric_in(U_85,relation_field(U_85)) )
& ( is_antisymmetric_in(U_85,relation_field(U_85))
| ~ antisymmetric(U_85) ) )
| ~ relation(U_85) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( is_antisymmetric_in(U_85,relation_field(U_85))
| ~ antisymmetric(U_85)
| ~ relation(U_85) ),
inference(clausify,[status(thm)],[f_18_2]) ).
cnf(f_18_4,plain,
( antisymmetric(U_85)
| ~ is_antisymmetric_in(U_85,relation_field(U_85))
| ~ relation(U_85) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [A] :
( ! [B,C] :
( ( C = relation_inverse_image(A,B)
| ? [D] :
( ( ~ in(D,C)
& in(apply(A,D),B)
& in(D,relation_dom(A)) )
| ( ( ~ in(apply(A,D),B)
| ~ in(D,relation_dom(A)) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ~ in(apply(A,D),B)
| ~ in(D,relation_dom(A)) )
& ( ( in(apply(A,D),B)
& in(D,relation_dom(A)) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d13_funct_1]) ).
fof(f_19_2,plain,
! [U_90] :
( ! [U_89,U_88] :
( ( U_88 = relation_inverse_image(U_90,U_89)
| ? [U_87] :
( ( ~ in(U_87,U_88)
& in(apply(U_90,U_87),U_89)
& in(U_87,relation_dom(U_90)) )
| ( ( ~ in(apply(U_90,U_87),U_89)
| ~ in(U_87,relation_dom(U_90)) )
& in(U_87,U_88) ) ) )
& ( ! [U_86] :
( ( in(U_86,U_88)
| ~ in(apply(U_90,U_86),U_89)
| ~ in(U_86,relation_dom(U_90)) )
& ( ( in(apply(U_90,U_86),U_89)
& in(U_86,relation_dom(U_90)) )
| ~ in(U_86,U_88) ) )
| U_88 != relation_inverse_image(U_90,U_89) ) )
| ~ function(U_90)
| ~ relation(U_90) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_90] :
( ( ! [U_98,U_96] :
( U_96 = relation_inverse_image(U_90,U_98)
| ? [U_94] :
( ~ in(U_94,U_96)
& in(apply(U_90,U_94),U_98)
& in(U_94,relation_dom(U_90)) )
| ? [U_93] :
( ( ~ in(apply(U_90,U_93),U_98)
| ~ in(U_93,relation_dom(U_90)) )
& in(U_93,U_96) ) )
& ! [U_97,U_95] :
( ( ! [U_92] :
( in(U_92,U_95)
| ~ in(apply(U_90,U_92),U_97)
| ~ in(U_92,relation_dom(U_90)) )
& ! [U_91] :
( ( in(apply(U_90,U_91),U_97)
& in(U_91,relation_dom(U_90)) )
| ~ in(U_91,U_95) ) )
| U_95 != relation_inverse_image(U_90,U_97) ) )
| ~ function(U_90)
| ~ relation(U_90) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
fof(f_19_4,plain,
! [U_90] :
( ( ! [U_98,U_96] :
( U_96 = relation_inverse_image(U_90,U_98)
| ? [U_94] :
( ~ in(U_94,U_96)
& in(apply(U_90,U_94),U_98)
& in(U_94,relation_dom(U_90)) )
| ( ( ~ in(apply(U_90,sK17(U_90,U_98,U_96)),U_98)
| ~ in(sK17(U_90,U_98,U_96),relation_dom(U_90)) )
& in(sK17(U_90,U_98,U_96),U_96) ) )
& ! [U_97,U_95] :
( ( ! [U_92] :
( in(U_92,U_95)
| ~ in(apply(U_90,U_92),U_97)
| ~ in(U_92,relation_dom(U_90)) )
& ! [U_91] :
( ( in(apply(U_90,U_91),U_97)
& in(U_91,relation_dom(U_90)) )
| ~ in(U_91,U_95) ) )
| U_95 != relation_inverse_image(U_90,U_97) ) )
| ~ function(U_90)
| ~ relation(U_90) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_93,sK17(U_90,U_98,U_96))],[f_19_3]) ).
fof(f_19_5,plain,
! [U_90] :
( ( ! [U_98,U_96] :
( U_96 = relation_inverse_image(U_90,U_98)
| ( ~ in(sK18(U_90,U_98,U_96),U_96)
& in(apply(U_90,sK18(U_90,U_98,U_96)),U_98)
& in(sK18(U_90,U_98,U_96),relation_dom(U_90)) )
| ( ( ~ in(apply(U_90,sK17(U_90,U_98,U_96)),U_98)
| ~ in(sK17(U_90,U_98,U_96),relation_dom(U_90)) )
& in(sK17(U_90,U_98,U_96),U_96) ) )
& ! [U_97,U_95] :
( ( ! [U_92] :
( in(U_92,U_95)
| ~ in(apply(U_90,U_92),U_97)
| ~ in(U_92,relation_dom(U_90)) )
& ! [U_91] :
( ( in(apply(U_90,U_91),U_97)
& in(U_91,relation_dom(U_90)) )
| ~ in(U_91,U_95) ) )
| U_95 != relation_inverse_image(U_90,U_97) ) )
| ~ function(U_90)
| ~ relation(U_90) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_94,sK18(U_90,U_98,U_96))],[f_19_4]) ).
cnf(f_19_6,plain,
( in(U_91,relation_dom(U_90))
| ~ in(U_91,U_95)
| U_95 != relation_inverse_image(U_90,U_97)
| ~ function(U_90)
| ~ relation(U_90) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_7,plain,
( in(apply(U_90,U_91),U_97)
| ~ in(U_91,U_95)
| U_95 != relation_inverse_image(U_90,U_97)
| ~ function(U_90)
| ~ relation(U_90) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_8,plain,
( in(U_92,U_95)
| ~ in(apply(U_90,U_92),U_97)
| ~ in(U_92,relation_dom(U_90))
| U_95 != relation_inverse_image(U_90,U_97)
| ~ function(U_90)
| ~ relation(U_90) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_9,plain,
( in(sK18(U_90,U_98,U_96),relation_dom(U_90))
| in(sK17(U_90,U_98,U_96),U_96)
| U_96 = relation_inverse_image(U_90,U_98)
| ~ function(U_90)
| ~ relation(U_90) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_10,plain,
( in(apply(U_90,sK18(U_90,U_98,U_96)),U_98)
| in(sK17(U_90,U_98,U_96),U_96)
| U_96 = relation_inverse_image(U_90,U_98)
| ~ function(U_90)
| ~ relation(U_90) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_11,plain,
( ~ in(sK18(U_90,U_98,U_96),U_96)
| in(sK17(U_90,U_98,U_96),U_96)
| U_96 = relation_inverse_image(U_90,U_98)
| ~ function(U_90)
| ~ relation(U_90) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_12,plain,
( in(sK18(U_90,U_98,U_96),relation_dom(U_90))
| ~ in(apply(U_90,sK17(U_90,U_98,U_96)),U_98)
| ~ in(sK17(U_90,U_98,U_96),relation_dom(U_90))
| U_96 = relation_inverse_image(U_90,U_98)
| ~ function(U_90)
| ~ relation(U_90) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_13,plain,
( in(apply(U_90,sK18(U_90,U_98,U_96)),U_98)
| ~ in(apply(U_90,sK17(U_90,U_98,U_96)),U_98)
| ~ in(sK17(U_90,U_98,U_96),relation_dom(U_90))
| U_96 = relation_inverse_image(U_90,U_98)
| ~ function(U_90)
| ~ relation(U_90) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_14,plain,
( ~ in(sK18(U_90,U_98,U_96),U_96)
| ~ in(apply(U_90,sK17(U_90,U_98,U_96)),U_98)
| ~ in(sK17(U_90,U_98,U_96),relation_dom(U_90))
| U_96 = relation_inverse_image(U_90,U_98)
| ~ function(U_90)
| ~ relation(U_90) ),
inference(clausify,[status(thm)],[f_19_5]) ).
fof(f_20_1,plain,
! [A] :
( ! [B,C] :
( ( C = relation_image(A,B)
| ? [D] :
( ( ~ in(D,C)
& ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) ) )
| ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) ) )
& ( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d13_relat_1]) ).
fof(f_20_2,plain,
! [U_107] :
( ! [U_106,U_105] :
( ( U_105 = relation_image(U_107,U_106)
| ? [U_104] :
( ( ~ in(U_104,U_105)
& ? [U_103] :
( in(U_103,U_106)
& in(ordered_pair(U_103,U_104),U_107) ) )
| ( ! [U_102] :
( ~ in(U_102,U_106)
| ~ in(ordered_pair(U_102,U_104),U_107) )
& in(U_104,U_105) ) ) )
& ( ! [U_101] :
( ( in(U_101,U_105)
| ! [U_100] :
( ~ in(U_100,U_106)
| ~ in(ordered_pair(U_100,U_101),U_107) ) )
& ( ? [U_99] :
( in(U_99,U_106)
& in(ordered_pair(U_99,U_101),U_107) )
| ~ in(U_101,U_105) ) )
| U_105 != relation_image(U_107,U_106) ) )
| ~ relation(U_107) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_107] :
( ( ! [U_115,U_113] :
( U_113 = relation_image(U_107,U_115)
| ? [U_111] :
( ~ in(U_111,U_113)
& ? [U_103] :
( in(U_103,U_115)
& in(ordered_pair(U_103,U_111),U_107) ) )
| ? [U_110] :
( ! [U_102] :
( ~ in(U_102,U_115)
| ~ in(ordered_pair(U_102,U_110),U_107) )
& in(U_110,U_113) ) )
& ! [U_114,U_112] :
( ( ! [U_109] :
( in(U_109,U_112)
| ! [U_100] :
( ~ in(U_100,U_114)
| ~ in(ordered_pair(U_100,U_109),U_107) ) )
& ! [U_108] :
( ? [U_99] :
( in(U_99,U_114)
& in(ordered_pair(U_99,U_108),U_107) )
| ~ in(U_108,U_112) ) )
| U_112 != relation_image(U_107,U_114) ) )
| ~ relation(U_107) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
fof(f_20_4,plain,
! [U_107] :
( ( ! [U_115,U_113] :
( U_113 = relation_image(U_107,U_115)
| ? [U_111] :
( ~ in(U_111,U_113)
& ? [U_103] :
( in(U_103,U_115)
& in(ordered_pair(U_103,U_111),U_107) ) )
| ? [U_110] :
( ! [U_102] :
( ~ in(U_102,U_115)
| ~ in(ordered_pair(U_102,U_110),U_107) )
& in(U_110,U_113) ) )
& ! [U_114,U_112] :
( ( ! [U_109] :
( in(U_109,U_112)
| ! [U_100] :
( ~ in(U_100,U_114)
| ~ in(ordered_pair(U_100,U_109),U_107) ) )
& ! [U_108] :
( ( in(sK19(U_107,U_114,U_112,U_108),U_114)
& in(ordered_pair(sK19(U_107,U_114,U_112,U_108),U_108),U_107) )
| ~ in(U_108,U_112) ) )
| U_112 != relation_image(U_107,U_114) ) )
| ~ relation(U_107) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_99,sK19(U_107,U_114,U_112,U_108))],[f_20_3]) ).
fof(f_20_5,plain,
! [U_107] :
( ( ! [U_115,U_113] :
( U_113 = relation_image(U_107,U_115)
| ? [U_111] :
( ~ in(U_111,U_113)
& ? [U_103] :
( in(U_103,U_115)
& in(ordered_pair(U_103,U_111),U_107) ) )
| ( ! [U_102] :
( ~ in(U_102,U_115)
| ~ in(ordered_pair(U_102,sK20(U_107,U_115,U_113)),U_107) )
& in(sK20(U_107,U_115,U_113),U_113) ) )
& ! [U_114,U_112] :
( ( ! [U_109] :
( in(U_109,U_112)
| ! [U_100] :
( ~ in(U_100,U_114)
| ~ in(ordered_pair(U_100,U_109),U_107) ) )
& ! [U_108] :
( ( in(sK19(U_107,U_114,U_112,U_108),U_114)
& in(ordered_pair(sK19(U_107,U_114,U_112,U_108),U_108),U_107) )
| ~ in(U_108,U_112) ) )
| U_112 != relation_image(U_107,U_114) ) )
| ~ relation(U_107) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_110,sK20(U_107,U_115,U_113))],[f_20_4]) ).
fof(f_20_6,plain,
! [U_107] :
( ( ! [U_115,U_113] :
( U_113 = relation_image(U_107,U_115)
| ( ~ in(sK21(U_107,U_115,U_113),U_113)
& ? [U_103] :
( in(U_103,U_115)
& in(ordered_pair(U_103,sK21(U_107,U_115,U_113)),U_107) ) )
| ( ! [U_102] :
( ~ in(U_102,U_115)
| ~ in(ordered_pair(U_102,sK20(U_107,U_115,U_113)),U_107) )
& in(sK20(U_107,U_115,U_113),U_113) ) )
& ! [U_114,U_112] :
( ( ! [U_109] :
( in(U_109,U_112)
| ! [U_100] :
( ~ in(U_100,U_114)
| ~ in(ordered_pair(U_100,U_109),U_107) ) )
& ! [U_108] :
( ( in(sK19(U_107,U_114,U_112,U_108),U_114)
& in(ordered_pair(sK19(U_107,U_114,U_112,U_108),U_108),U_107) )
| ~ in(U_108,U_112) ) )
| U_112 != relation_image(U_107,U_114) ) )
| ~ relation(U_107) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_111,sK21(U_107,U_115,U_113))],[f_20_5]) ).
fof(f_20_7,plain,
! [U_107] :
( ( ! [U_115,U_113] :
( U_113 = relation_image(U_107,U_115)
| ( ~ in(sK21(U_107,U_115,U_113),U_113)
& in(sK22(U_107,U_115,U_113),U_115)
& in(ordered_pair(sK22(U_107,U_115,U_113),sK21(U_107,U_115,U_113)),U_107) )
| ( ! [U_102] :
( ~ in(U_102,U_115)
| ~ in(ordered_pair(U_102,sK20(U_107,U_115,U_113)),U_107) )
& in(sK20(U_107,U_115,U_113),U_113) ) )
& ! [U_114,U_112] :
( ( ! [U_109] :
( in(U_109,U_112)
| ! [U_100] :
( ~ in(U_100,U_114)
| ~ in(ordered_pair(U_100,U_109),U_107) ) )
& ! [U_108] :
( ( in(sK19(U_107,U_114,U_112,U_108),U_114)
& in(ordered_pair(sK19(U_107,U_114,U_112,U_108),U_108),U_107) )
| ~ in(U_108,U_112) ) )
| U_112 != relation_image(U_107,U_114) ) )
| ~ relation(U_107) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_103,sK22(U_107,U_115,U_113))],[f_20_6]) ).
cnf(f_20_8,plain,
( in(ordered_pair(sK19(U_107,U_114,U_112,U_108),U_108),U_107)
| ~ in(U_108,U_112)
| U_112 != relation_image(U_107,U_114)
| ~ relation(U_107) ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_9,plain,
( in(sK19(U_107,U_114,U_112,U_108),U_114)
| ~ in(U_108,U_112)
| U_112 != relation_image(U_107,U_114)
| ~ relation(U_107) ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_10,plain,
( in(U_109,U_112)
| ~ in(U_100,U_114)
| ~ in(ordered_pair(U_100,U_109),U_107)
| U_112 != relation_image(U_107,U_114)
| ~ relation(U_107) ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_11,plain,
( in(ordered_pair(sK22(U_107,U_115,U_113),sK21(U_107,U_115,U_113)),U_107)
| in(sK20(U_107,U_115,U_113),U_113)
| U_113 = relation_image(U_107,U_115)
| ~ relation(U_107) ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_12,plain,
( in(sK22(U_107,U_115,U_113),U_115)
| in(sK20(U_107,U_115,U_113),U_113)
| U_113 = relation_image(U_107,U_115)
| ~ relation(U_107) ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_13,plain,
( ~ in(sK21(U_107,U_115,U_113),U_113)
| in(sK20(U_107,U_115,U_113),U_113)
| U_113 = relation_image(U_107,U_115)
| ~ relation(U_107) ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_14,plain,
( in(ordered_pair(sK22(U_107,U_115,U_113),sK21(U_107,U_115,U_113)),U_107)
| ~ in(U_102,U_115)
| ~ in(ordered_pair(U_102,sK20(U_107,U_115,U_113)),U_107)
| U_113 = relation_image(U_107,U_115)
| ~ relation(U_107) ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_15,plain,
( in(sK22(U_107,U_115,U_113),U_115)
| ~ in(U_102,U_115)
| ~ in(ordered_pair(U_102,sK20(U_107,U_115,U_113)),U_107)
| U_113 = relation_image(U_107,U_115)
| ~ relation(U_107) ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_16,plain,
( ~ in(sK21(U_107,U_115,U_113),U_113)
| ~ in(U_102,U_115)
| ~ in(ordered_pair(U_102,sK20(U_107,U_115,U_113)),U_107)
| U_113 = relation_image(U_107,U_115)
| ~ relation(U_107) ),
inference(clausify,[status(thm)],[f_20_7]) ).
fof(f_21_1,plain,
! [A] :
( ! [B,C] :
( ( C = relation_inverse_image(A,B)
| ? [D] :
( ( ~ in(D,C)
& ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) ) )
| ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) ) )
& ( ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d14_relat_1]) ).
fof(f_21_2,plain,
! [U_124] :
( ! [U_123,U_122] :
( ( U_122 = relation_inverse_image(U_124,U_123)
| ? [U_121] :
( ( ~ in(U_121,U_122)
& ? [U_120] :
( in(U_120,U_123)
& in(ordered_pair(U_121,U_120),U_124) ) )
| ( ! [U_119] :
( ~ in(U_119,U_123)
| ~ in(ordered_pair(U_121,U_119),U_124) )
& in(U_121,U_122) ) ) )
& ( ! [U_118] :
( ( in(U_118,U_122)
| ! [U_117] :
( ~ in(U_117,U_123)
| ~ in(ordered_pair(U_118,U_117),U_124) ) )
& ( ? [U_116] :
( in(U_116,U_123)
& in(ordered_pair(U_118,U_116),U_124) )
| ~ in(U_118,U_122) ) )
| U_122 != relation_inverse_image(U_124,U_123) ) )
| ~ relation(U_124) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_124] :
( ( ! [U_132,U_130] :
( U_130 = relation_inverse_image(U_124,U_132)
| ? [U_128] :
( ~ in(U_128,U_130)
& ? [U_120] :
( in(U_120,U_132)
& in(ordered_pair(U_128,U_120),U_124) ) )
| ? [U_127] :
( ! [U_119] :
( ~ in(U_119,U_132)
| ~ in(ordered_pair(U_127,U_119),U_124) )
& in(U_127,U_130) ) )
& ! [U_131,U_129] :
( ( ! [U_126] :
( in(U_126,U_129)
| ! [U_117] :
( ~ in(U_117,U_131)
| ~ in(ordered_pair(U_126,U_117),U_124) ) )
& ! [U_125] :
( ? [U_116] :
( in(U_116,U_131)
& in(ordered_pair(U_125,U_116),U_124) )
| ~ in(U_125,U_129) ) )
| U_129 != relation_inverse_image(U_124,U_131) ) )
| ~ relation(U_124) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
fof(f_21_4,plain,
! [U_124] :
( ( ! [U_132,U_130] :
( U_130 = relation_inverse_image(U_124,U_132)
| ? [U_128] :
( ~ in(U_128,U_130)
& ? [U_120] :
( in(U_120,U_132)
& in(ordered_pair(U_128,U_120),U_124) ) )
| ? [U_127] :
( ! [U_119] :
( ~ in(U_119,U_132)
| ~ in(ordered_pair(U_127,U_119),U_124) )
& in(U_127,U_130) ) )
& ! [U_131,U_129] :
( ( ! [U_126] :
( in(U_126,U_129)
| ! [U_117] :
( ~ in(U_117,U_131)
| ~ in(ordered_pair(U_126,U_117),U_124) ) )
& ! [U_125] :
( ( in(sK23(U_124,U_131,U_129,U_125),U_131)
& in(ordered_pair(U_125,sK23(U_124,U_131,U_129,U_125)),U_124) )
| ~ in(U_125,U_129) ) )
| U_129 != relation_inverse_image(U_124,U_131) ) )
| ~ relation(U_124) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_116,sK23(U_124,U_131,U_129,U_125))],[f_21_3]) ).
fof(f_21_5,plain,
! [U_124] :
( ( ! [U_132,U_130] :
( U_130 = relation_inverse_image(U_124,U_132)
| ? [U_128] :
( ~ in(U_128,U_130)
& ? [U_120] :
( in(U_120,U_132)
& in(ordered_pair(U_128,U_120),U_124) ) )
| ( ! [U_119] :
( ~ in(U_119,U_132)
| ~ in(ordered_pair(sK24(U_124,U_132,U_130),U_119),U_124) )
& in(sK24(U_124,U_132,U_130),U_130) ) )
& ! [U_131,U_129] :
( ( ! [U_126] :
( in(U_126,U_129)
| ! [U_117] :
( ~ in(U_117,U_131)
| ~ in(ordered_pair(U_126,U_117),U_124) ) )
& ! [U_125] :
( ( in(sK23(U_124,U_131,U_129,U_125),U_131)
& in(ordered_pair(U_125,sK23(U_124,U_131,U_129,U_125)),U_124) )
| ~ in(U_125,U_129) ) )
| U_129 != relation_inverse_image(U_124,U_131) ) )
| ~ relation(U_124) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_127,sK24(U_124,U_132,U_130))],[f_21_4]) ).
fof(f_21_6,plain,
! [U_124] :
( ( ! [U_132,U_130] :
( U_130 = relation_inverse_image(U_124,U_132)
| ( ~ in(sK25(U_124,U_132,U_130),U_130)
& ? [U_120] :
( in(U_120,U_132)
& in(ordered_pair(sK25(U_124,U_132,U_130),U_120),U_124) ) )
| ( ! [U_119] :
( ~ in(U_119,U_132)
| ~ in(ordered_pair(sK24(U_124,U_132,U_130),U_119),U_124) )
& in(sK24(U_124,U_132,U_130),U_130) ) )
& ! [U_131,U_129] :
( ( ! [U_126] :
( in(U_126,U_129)
| ! [U_117] :
( ~ in(U_117,U_131)
| ~ in(ordered_pair(U_126,U_117),U_124) ) )
& ! [U_125] :
( ( in(sK23(U_124,U_131,U_129,U_125),U_131)
& in(ordered_pair(U_125,sK23(U_124,U_131,U_129,U_125)),U_124) )
| ~ in(U_125,U_129) ) )
| U_129 != relation_inverse_image(U_124,U_131) ) )
| ~ relation(U_124) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_128,sK25(U_124,U_132,U_130))],[f_21_5]) ).
fof(f_21_7,plain,
! [U_124] :
( ( ! [U_132,U_130] :
( U_130 = relation_inverse_image(U_124,U_132)
| ( ~ in(sK25(U_124,U_132,U_130),U_130)
& in(sK26(U_124,U_132,U_130),U_132)
& in(ordered_pair(sK25(U_124,U_132,U_130),sK26(U_124,U_132,U_130)),U_124) )
| ( ! [U_119] :
( ~ in(U_119,U_132)
| ~ in(ordered_pair(sK24(U_124,U_132,U_130),U_119),U_124) )
& in(sK24(U_124,U_132,U_130),U_130) ) )
& ! [U_131,U_129] :
( ( ! [U_126] :
( in(U_126,U_129)
| ! [U_117] :
( ~ in(U_117,U_131)
| ~ in(ordered_pair(U_126,U_117),U_124) ) )
& ! [U_125] :
( ( in(sK23(U_124,U_131,U_129,U_125),U_131)
& in(ordered_pair(U_125,sK23(U_124,U_131,U_129,U_125)),U_124) )
| ~ in(U_125,U_129) ) )
| U_129 != relation_inverse_image(U_124,U_131) ) )
| ~ relation(U_124) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_120,sK26(U_124,U_132,U_130))],[f_21_6]) ).
cnf(f_21_8,plain,
( in(ordered_pair(U_125,sK23(U_124,U_131,U_129,U_125)),U_124)
| ~ in(U_125,U_129)
| U_129 != relation_inverse_image(U_124,U_131)
| ~ relation(U_124) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_9,plain,
( in(sK23(U_124,U_131,U_129,U_125),U_131)
| ~ in(U_125,U_129)
| U_129 != relation_inverse_image(U_124,U_131)
| ~ relation(U_124) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_10,plain,
( in(U_126,U_129)
| ~ in(U_117,U_131)
| ~ in(ordered_pair(U_126,U_117),U_124)
| U_129 != relation_inverse_image(U_124,U_131)
| ~ relation(U_124) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_11,plain,
( in(ordered_pair(sK25(U_124,U_132,U_130),sK26(U_124,U_132,U_130)),U_124)
| in(sK24(U_124,U_132,U_130),U_130)
| U_130 = relation_inverse_image(U_124,U_132)
| ~ relation(U_124) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_12,plain,
( in(sK26(U_124,U_132,U_130),U_132)
| in(sK24(U_124,U_132,U_130),U_130)
| U_130 = relation_inverse_image(U_124,U_132)
| ~ relation(U_124) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_13,plain,
( ~ in(sK25(U_124,U_132,U_130),U_130)
| in(sK24(U_124,U_132,U_130),U_130)
| U_130 = relation_inverse_image(U_124,U_132)
| ~ relation(U_124) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_14,plain,
( in(ordered_pair(sK25(U_124,U_132,U_130),sK26(U_124,U_132,U_130)),U_124)
| ~ in(U_119,U_132)
| ~ in(ordered_pair(sK24(U_124,U_132,U_130),U_119),U_124)
| U_130 = relation_inverse_image(U_124,U_132)
| ~ relation(U_124) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_15,plain,
( in(sK26(U_124,U_132,U_130),U_132)
| ~ in(U_119,U_132)
| ~ in(ordered_pair(sK24(U_124,U_132,U_130),U_119),U_124)
| U_130 = relation_inverse_image(U_124,U_132)
| ~ relation(U_124) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_16,plain,
( ~ in(sK25(U_124,U_132,U_130),U_130)
| ~ in(U_119,U_132)
| ~ in(ordered_pair(sK24(U_124,U_132,U_130),U_119),U_124)
| U_130 = relation_inverse_image(U_124,U_132)
| ~ relation(U_124) ),
inference(clausify,[status(thm)],[f_21_7]) ).
fof(f_22_1,plain,
! [A] :
( ( ( connected(A)
| ~ is_connected_in(A,relation_field(A)) )
& ( is_connected_in(A,relation_field(A))
| ~ connected(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d14_relat_2]) ).
fof(f_22_2,plain,
! [U_133] :
( ( ( connected(U_133)
| ~ is_connected_in(U_133,relation_field(U_133)) )
& ( is_connected_in(U_133,relation_field(U_133))
| ~ connected(U_133) ) )
| ~ relation(U_133) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( is_connected_in(U_133,relation_field(U_133))
| ~ connected(U_133)
| ~ relation(U_133) ),
inference(clausify,[status(thm)],[f_22_2]) ).
cnf(f_22_4,plain,
( connected(U_133)
| ~ is_connected_in(U_133,relation_field(U_133))
| ~ relation(U_133) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [A] :
( ( ( transitive(A)
| ~ is_transitive_in(A,relation_field(A)) )
& ( is_transitive_in(A,relation_field(A))
| ~ transitive(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d16_relat_2]) ).
fof(f_23_2,plain,
! [U_134] :
( ( ( transitive(U_134)
| ~ is_transitive_in(U_134,relation_field(U_134)) )
& ( is_transitive_in(U_134,relation_field(U_134))
| ~ transitive(U_134) ) )
| ~ relation(U_134) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( is_transitive_in(U_134,relation_field(U_134))
| ~ transitive(U_134)
| ~ relation(U_134) ),
inference(clausify,[status(thm)],[f_23_2]) ).
cnf(f_23_4,plain,
( transitive(U_134)
| ~ is_transitive_in(U_134,relation_field(U_134))
| ~ relation(U_134) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
! [A,B,C,D] :
( ( D = unordered_triple(A,B,C)
| ? [E] :
( ( ~ in(E,D)
& ( E = C
| E = B
| E = A ) )
| ( E != C
& E != B
& E != A
& in(E,D) ) ) )
& ( ! [E] :
( ( in(E,D)
| ( E != C
& E != B
& E != A ) )
& ( E = C
| E = B
| E = A
| ~ in(E,D) ) )
| D != unordered_triple(A,B,C) ) ),
inference(fof_nnf,[status(thm)],[d1_enumset1]) ).
fof(f_24_2,plain,
! [U_140,U_139,U_138,U_137] :
( ( U_137 = unordered_triple(U_140,U_139,U_138)
| ? [U_136] :
( ( ~ in(U_136,U_137)
& ( U_136 = U_138
| U_136 = U_139
| U_136 = U_140 ) )
| ( U_136 != U_138
& U_136 != U_139
& U_136 != U_140
& in(U_136,U_137) ) ) )
& ( ! [U_135] :
( ( in(U_135,U_137)
| ( U_135 != U_138
& U_135 != U_139
& U_135 != U_140 ) )
& ( U_135 = U_138
| U_135 = U_139
| U_135 = U_140
| ~ in(U_135,U_137) ) )
| U_137 != unordered_triple(U_140,U_139,U_138) ) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( ! [U_152,U_150,U_148,U_146] :
( U_146 = unordered_triple(U_152,U_150,U_148)
| ? [U_144] :
( ~ in(U_144,U_146)
& ( U_144 = U_148
| U_144 = U_150
| U_144 = U_152 ) )
| ? [U_143] :
( U_143 != U_148
& U_143 != U_150
& U_143 != U_152
& in(U_143,U_146) ) )
& ! [U_151,U_149,U_147,U_145] :
( ( ! [U_142] :
( in(U_142,U_145)
| ( U_142 != U_147
& U_142 != U_149
& U_142 != U_151 ) )
& ! [U_141] :
( U_141 = U_147
| U_141 = U_149
| U_141 = U_151
| ~ in(U_141,U_145) ) )
| U_145 != unordered_triple(U_151,U_149,U_147) ) ),
inference(miniscope,[status(thm)],[f_24_2]) ).
fof(f_24_4,plain,
( ! [U_152,U_150,U_148,U_146] :
( U_146 = unordered_triple(U_152,U_150,U_148)
| ? [U_144] :
( ~ in(U_144,U_146)
& ( U_144 = U_148
| U_144 = U_150
| U_144 = U_152 ) )
| ( sK27(U_152,U_150,U_148,U_146) != U_148
& sK27(U_152,U_150,U_148,U_146) != U_150
& sK27(U_152,U_150,U_148,U_146) != U_152
& in(sK27(U_152,U_150,U_148,U_146),U_146) ) )
& ! [U_151,U_149,U_147,U_145] :
( ( ! [U_142] :
( in(U_142,U_145)
| ( U_142 != U_147
& U_142 != U_149
& U_142 != U_151 ) )
& ! [U_141] :
( U_141 = U_147
| U_141 = U_149
| U_141 = U_151
| ~ in(U_141,U_145) ) )
| U_145 != unordered_triple(U_151,U_149,U_147) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_143,sK27(U_152,U_150,U_148,U_146))],[f_24_3]) ).
fof(f_24_5,plain,
( ! [U_152,U_150,U_148,U_146] :
( U_146 = unordered_triple(U_152,U_150,U_148)
| ( ~ in(sK28(U_152,U_150,U_148,U_146),U_146)
& ( sK28(U_152,U_150,U_148,U_146) = U_148
| sK28(U_152,U_150,U_148,U_146) = U_150
| sK28(U_152,U_150,U_148,U_146) = U_152 ) )
| ( sK27(U_152,U_150,U_148,U_146) != U_148
& sK27(U_152,U_150,U_148,U_146) != U_150
& sK27(U_152,U_150,U_148,U_146) != U_152
& in(sK27(U_152,U_150,U_148,U_146),U_146) ) )
& ! [U_151,U_149,U_147,U_145] :
( ( ! [U_142] :
( in(U_142,U_145)
| ( U_142 != U_147
& U_142 != U_149
& U_142 != U_151 ) )
& ! [U_141] :
( U_141 = U_147
| U_141 = U_149
| U_141 = U_151
| ~ in(U_141,U_145) ) )
| U_145 != unordered_triple(U_151,U_149,U_147) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_144,sK28(U_152,U_150,U_148,U_146))],[f_24_4]) ).
cnf(f_24_6,plain,
( U_141 = U_147
| U_141 = U_149
| U_141 = U_151
| ~ in(U_141,U_145)
| U_145 != unordered_triple(U_151,U_149,U_147) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_7,plain,
( U_142 != U_151
| in(U_142,U_145)
| U_145 != unordered_triple(U_151,U_149,U_147) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_8,plain,
( U_142 != U_149
| in(U_142,U_145)
| U_145 != unordered_triple(U_151,U_149,U_147) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_9,plain,
( U_142 != U_147
| in(U_142,U_145)
| U_145 != unordered_triple(U_151,U_149,U_147) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_10,plain,
( sK28(U_152,U_150,U_148,U_146) = U_148
| sK28(U_152,U_150,U_148,U_146) = U_150
| sK28(U_152,U_150,U_148,U_146) = U_152
| in(sK27(U_152,U_150,U_148,U_146),U_146)
| U_146 = unordered_triple(U_152,U_150,U_148) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_11,plain,
( ~ in(sK28(U_152,U_150,U_148,U_146),U_146)
| in(sK27(U_152,U_150,U_148,U_146),U_146)
| U_146 = unordered_triple(U_152,U_150,U_148) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_12,plain,
( sK27(U_152,U_150,U_148,U_146) != U_152
| sK28(U_152,U_150,U_148,U_146) = U_148
| sK28(U_152,U_150,U_148,U_146) = U_150
| sK28(U_152,U_150,U_148,U_146) = U_152
| U_146 = unordered_triple(U_152,U_150,U_148) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_13,plain,
( sK27(U_152,U_150,U_148,U_146) != U_150
| sK28(U_152,U_150,U_148,U_146) = U_148
| sK28(U_152,U_150,U_148,U_146) = U_150
| sK28(U_152,U_150,U_148,U_146) = U_152
| U_146 = unordered_triple(U_152,U_150,U_148) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_14,plain,
( sK27(U_152,U_150,U_148,U_146) != U_148
| sK28(U_152,U_150,U_148,U_146) = U_148
| sK28(U_152,U_150,U_148,U_146) = U_150
| sK28(U_152,U_150,U_148,U_146) = U_152
| U_146 = unordered_triple(U_152,U_150,U_148) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_15,plain,
( sK27(U_152,U_150,U_148,U_146) != U_152
| ~ in(sK28(U_152,U_150,U_148,U_146),U_146)
| U_146 = unordered_triple(U_152,U_150,U_148) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_16,plain,
( sK27(U_152,U_150,U_148,U_146) != U_150
| ~ in(sK28(U_152,U_150,U_148,U_146),U_146)
| U_146 = unordered_triple(U_152,U_150,U_148) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_17,plain,
( sK27(U_152,U_150,U_148,U_146) != U_148
| ~ in(sK28(U_152,U_150,U_148,U_146),U_146)
| U_146 = unordered_triple(U_152,U_150,U_148) ),
inference(clausify,[status(thm)],[f_24_5]) ).
fof(f_25_1,plain,
! [A] : succ(A) = set_union2(A,singleton(A)),
inference(fof_nnf,[status(thm)],[d1_ordinal1]) ).
fof(f_25_2,plain,
! [U_153] : succ(U_153) = set_union2(U_153,singleton(U_153)),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
succ(U_153) = set_union2(U_153,singleton(U_153)),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
! [A] :
( ( relation(A)
| ? [B] :
( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) ) )
& ( ! [B] :
( ? [C,D] : B = ordered_pair(C,D)
| ~ in(B,A) )
| ~ relation(A) ) ),
inference(fof_nnf,[status(thm)],[d1_relat_1]) ).
fof(f_26_2,plain,
! [U_160] :
( ( relation(U_160)
| ? [U_159] :
( ! [U_158,U_157] : U_159 != ordered_pair(U_158,U_157)
& in(U_159,U_160) ) )
& ( ! [U_156] :
( ? [U_155,U_154] : U_156 = ordered_pair(U_155,U_154)
| ~ in(U_156,U_160) )
| ~ relation(U_160) ) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( ! [U_162] :
( relation(U_162)
| ? [U_159] :
( ! [U_158,U_157] : U_159 != ordered_pair(U_158,U_157)
& in(U_159,U_162) ) )
& ! [U_161] :
( ! [U_156] :
( ? [U_155,U_154] : U_156 = ordered_pair(U_155,U_154)
| ~ in(U_156,U_161) )
| ~ relation(U_161) ) ),
inference(miniscope,[status(thm)],[f_26_2]) ).
fof(f_26_4,plain,
( ! [U_162] :
( relation(U_162)
| ? [U_159] :
( ! [U_158,U_157] : U_159 != ordered_pair(U_158,U_157)
& in(U_159,U_162) ) )
& ! [U_161] :
( ! [U_156] :
( ? [U_154] : U_156 = ordered_pair(sK29(U_161,U_156),U_154)
| ~ in(U_156,U_161) )
| ~ relation(U_161) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_155,sK29(U_161,U_156))],[f_26_3]) ).
fof(f_26_5,plain,
( ! [U_162] :
( relation(U_162)
| ? [U_159] :
( ! [U_158,U_157] : U_159 != ordered_pair(U_158,U_157)
& in(U_159,U_162) ) )
& ! [U_161] :
( ! [U_156] :
( U_156 = ordered_pair(sK29(U_161,U_156),sK30(U_161,U_156))
| ~ in(U_156,U_161) )
| ~ relation(U_161) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_154,sK30(U_161,U_156))],[f_26_4]) ).
fof(f_26_6,plain,
( ! [U_162] :
( relation(U_162)
| ( ! [U_158,U_157] : sK31(U_162) != ordered_pair(U_158,U_157)
& in(sK31(U_162),U_162) ) )
& ! [U_161] :
( ! [U_156] :
( U_156 = ordered_pair(sK29(U_161,U_156),sK30(U_161,U_156))
| ~ in(U_156,U_161) )
| ~ relation(U_161) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_159,sK31(U_162))],[f_26_5]) ).
cnf(f_26_7,plain,
( U_156 = ordered_pair(sK29(U_161,U_156),sK30(U_161,U_156))
| ~ in(U_156,U_161)
| ~ relation(U_161) ),
inference(clausify,[status(thm)],[f_26_6]) ).
cnf(f_26_8,plain,
( in(sK31(U_162),U_162)
| relation(U_162) ),
inference(clausify,[status(thm)],[f_26_6]) ).
cnf(f_26_9,plain,
( sK31(U_162) != ordered_pair(U_158,U_157)
| relation(U_162) ),
inference(clausify,[status(thm)],[f_26_6]) ).
fof(f_27_1,plain,
! [A] :
( ! [B] :
( ( is_reflexive_in(A,B)
| ? [C] :
( ~ in(ordered_pair(C,C),A)
& in(C,B) ) )
& ( ! [C] :
( in(ordered_pair(C,C),A)
| ~ in(C,B) )
| ~ is_reflexive_in(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d1_relat_2]) ).
fof(f_27_2,plain,
! [U_166] :
( ! [U_165] :
( ( is_reflexive_in(U_166,U_165)
| ? [U_164] :
( ~ in(ordered_pair(U_164,U_164),U_166)
& in(U_164,U_165) ) )
& ( ! [U_163] :
( in(ordered_pair(U_163,U_163),U_166)
| ~ in(U_163,U_165) )
| ~ is_reflexive_in(U_166,U_165) ) )
| ~ relation(U_166) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_166] :
( ( ! [U_168] :
( is_reflexive_in(U_166,U_168)
| ? [U_164] :
( ~ in(ordered_pair(U_164,U_164),U_166)
& in(U_164,U_168) ) )
& ! [U_167] :
( ! [U_163] :
( in(ordered_pair(U_163,U_163),U_166)
| ~ in(U_163,U_167) )
| ~ is_reflexive_in(U_166,U_167) ) )
| ~ relation(U_166) ),
inference(miniscope,[status(thm)],[f_27_2]) ).
fof(f_27_4,plain,
! [U_166] :
( ( ! [U_168] :
( is_reflexive_in(U_166,U_168)
| ( ~ in(ordered_pair(sK32(U_166,U_168),sK32(U_166,U_168)),U_166)
& in(sK32(U_166,U_168),U_168) ) )
& ! [U_167] :
( ! [U_163] :
( in(ordered_pair(U_163,U_163),U_166)
| ~ in(U_163,U_167) )
| ~ is_reflexive_in(U_166,U_167) ) )
| ~ relation(U_166) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_164,sK32(U_166,U_168))],[f_27_3]) ).
cnf(f_27_5,plain,
( in(ordered_pair(U_163,U_163),U_166)
| ~ in(U_163,U_167)
| ~ is_reflexive_in(U_166,U_167)
| ~ relation(U_166) ),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(f_27_6,plain,
( in(sK32(U_166,U_168),U_168)
| is_reflexive_in(U_166,U_168)
| ~ relation(U_166) ),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(f_27_7,plain,
( ~ in(ordered_pair(sK32(U_166,U_168),sK32(U_166,U_168)),U_166)
| is_reflexive_in(U_166,U_168)
| ~ relation(U_166) ),
inference(clausify,[status(thm)],[f_27_4]) ).
fof(f_28_1,plain,
! [A,B] :
( ( ( ( B = set_meet(A)
| B != empty_set )
& ( B = empty_set
| B != set_meet(A) ) )
| A != empty_set )
& ( ( ( B = set_meet(A)
| ? [C] :
( ( ~ in(C,B)
& ! [D] :
( in(C,D)
| ~ in(D,A) ) )
| ( ? [D] :
( ~ in(C,D)
& in(D,A) )
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ? [D] :
( ~ in(C,D)
& in(D,A) ) )
& ( ! [D] :
( in(C,D)
| ~ in(D,A) )
| ~ in(C,B) ) )
| B != set_meet(A) ) )
| A = empty_set ) ),
inference(fof_nnf,[status(thm)],[d1_setfam_1]) ).
fof(f_28_2,plain,
! [U_176,U_175] :
( ( ( ( U_175 = set_meet(U_176)
| U_175 != empty_set )
& ( U_175 = empty_set
| U_175 != set_meet(U_176) ) )
| U_176 != empty_set )
& ( ( ( U_175 = set_meet(U_176)
| ? [U_174] :
( ( ~ in(U_174,U_175)
& ! [U_173] :
( in(U_174,U_173)
| ~ in(U_173,U_176) ) )
| ( ? [U_172] :
( ~ in(U_174,U_172)
& in(U_172,U_176) )
& in(U_174,U_175) ) ) )
& ( ! [U_171] :
( ( in(U_171,U_175)
| ? [U_170] :
( ~ in(U_171,U_170)
& in(U_170,U_176) ) )
& ( ! [U_169] :
( in(U_171,U_169)
| ~ in(U_169,U_176) )
| ~ in(U_171,U_175) ) )
| U_175 != set_meet(U_176) ) )
| U_176 = empty_set ) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( ! [U_188] :
( ( ! [U_186] :
( U_186 = set_meet(U_188)
| U_186 != empty_set )
& ! [U_185] :
( U_185 = empty_set
| U_185 != set_meet(U_188) ) )
| U_188 != empty_set )
& ! [U_187] :
( ( ! [U_184] :
( U_184 = set_meet(U_187)
| ? [U_180] :
( ~ in(U_180,U_184)
& ! [U_173] :
( in(U_180,U_173)
| ~ in(U_173,U_187) ) )
| ? [U_179] :
( ? [U_172] :
( ~ in(U_179,U_172)
& in(U_172,U_187) )
& in(U_179,U_184) ) )
& ! [U_183] :
( ( ! [U_178] :
( in(U_178,U_183)
| ? [U_170] :
( ~ in(U_178,U_170)
& in(U_170,U_187) ) )
& ! [U_177] :
( ! [U_169] :
( in(U_177,U_169)
| ~ in(U_169,U_187) )
| ~ in(U_177,U_183) ) )
| U_183 != set_meet(U_187) ) )
| U_187 = empty_set ) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
fof(f_28_4,plain,
( ! [U_188] :
( ( ! [U_186] :
( U_186 = set_meet(U_188)
| U_186 != empty_set )
& ! [U_185] :
( U_185 = empty_set
| U_185 != set_meet(U_188) ) )
| U_188 != empty_set )
& ! [U_187] :
( ( ! [U_184] :
( U_184 = set_meet(U_187)
| ? [U_180] :
( ~ in(U_180,U_184)
& ! [U_173] :
( in(U_180,U_173)
| ~ in(U_173,U_187) ) )
| ? [U_179] :
( ? [U_172] :
( ~ in(U_179,U_172)
& in(U_172,U_187) )
& in(U_179,U_184) ) )
& ! [U_183] :
( ( ! [U_178] :
( in(U_178,U_183)
| ( ~ in(U_178,sK33(U_187,U_183,U_178))
& in(sK33(U_187,U_183,U_178),U_187) ) )
& ! [U_177] :
( ! [U_169] :
( in(U_177,U_169)
| ~ in(U_169,U_187) )
| ~ in(U_177,U_183) ) )
| U_183 != set_meet(U_187) ) )
| U_187 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_170,sK33(U_187,U_183,U_178))],[f_28_3]) ).
fof(f_28_5,plain,
( ! [U_188] :
( ( ! [U_186] :
( U_186 = set_meet(U_188)
| U_186 != empty_set )
& ! [U_185] :
( U_185 = empty_set
| U_185 != set_meet(U_188) ) )
| U_188 != empty_set )
& ! [U_187] :
( ( ! [U_184] :
( U_184 = set_meet(U_187)
| ? [U_180] :
( ~ in(U_180,U_184)
& ! [U_173] :
( in(U_180,U_173)
| ~ in(U_173,U_187) ) )
| ( ? [U_172] :
( ~ in(sK34(U_187,U_184),U_172)
& in(U_172,U_187) )
& in(sK34(U_187,U_184),U_184) ) )
& ! [U_183] :
( ( ! [U_178] :
( in(U_178,U_183)
| ( ~ in(U_178,sK33(U_187,U_183,U_178))
& in(sK33(U_187,U_183,U_178),U_187) ) )
& ! [U_177] :
( ! [U_169] :
( in(U_177,U_169)
| ~ in(U_169,U_187) )
| ~ in(U_177,U_183) ) )
| U_183 != set_meet(U_187) ) )
| U_187 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_179,sK34(U_187,U_184))],[f_28_4]) ).
fof(f_28_6,plain,
( ! [U_188] :
( ( ! [U_186] :
( U_186 = set_meet(U_188)
| U_186 != empty_set )
& ! [U_185] :
( U_185 = empty_set
| U_185 != set_meet(U_188) ) )
| U_188 != empty_set )
& ! [U_187] :
( ( ! [U_184] :
( U_184 = set_meet(U_187)
| ? [U_180] :
( ~ in(U_180,U_184)
& ! [U_173] :
( in(U_180,U_173)
| ~ in(U_173,U_187) ) )
| ( ~ in(sK34(U_187,U_184),sK35(U_187,U_184))
& in(sK35(U_187,U_184),U_187)
& in(sK34(U_187,U_184),U_184) ) )
& ! [U_183] :
( ( ! [U_178] :
( in(U_178,U_183)
| ( ~ in(U_178,sK33(U_187,U_183,U_178))
& in(sK33(U_187,U_183,U_178),U_187) ) )
& ! [U_177] :
( ! [U_169] :
( in(U_177,U_169)
| ~ in(U_169,U_187) )
| ~ in(U_177,U_183) ) )
| U_183 != set_meet(U_187) ) )
| U_187 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_172,sK35(U_187,U_184))],[f_28_5]) ).
fof(f_28_7,plain,
( ! [U_188] :
( ( ! [U_186] :
( U_186 = set_meet(U_188)
| U_186 != empty_set )
& ! [U_185] :
( U_185 = empty_set
| U_185 != set_meet(U_188) ) )
| U_188 != empty_set )
& ! [U_187] :
( ( ! [U_184] :
( U_184 = set_meet(U_187)
| ( ~ in(sK36(U_187,U_184),U_184)
& ! [U_173] :
( in(sK36(U_187,U_184),U_173)
| ~ in(U_173,U_187) ) )
| ( ~ in(sK34(U_187,U_184),sK35(U_187,U_184))
& in(sK35(U_187,U_184),U_187)
& in(sK34(U_187,U_184),U_184) ) )
& ! [U_183] :
( ( ! [U_178] :
( in(U_178,U_183)
| ( ~ in(U_178,sK33(U_187,U_183,U_178))
& in(sK33(U_187,U_183,U_178),U_187) ) )
& ! [U_177] :
( ! [U_169] :
( in(U_177,U_169)
| ~ in(U_169,U_187) )
| ~ in(U_177,U_183) ) )
| U_183 != set_meet(U_187) ) )
| U_187 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_180,sK36(U_187,U_184))],[f_28_6]) ).
cnf(f_28_8,plain,
( in(U_177,U_169)
| ~ in(U_169,U_187)
| ~ in(U_177,U_183)
| U_183 != set_meet(U_187)
| U_187 = empty_set ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_9,plain,
( in(sK33(U_187,U_183,U_178),U_187)
| in(U_178,U_183)
| U_183 != set_meet(U_187)
| U_187 = empty_set ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_10,plain,
( ~ in(U_178,sK33(U_187,U_183,U_178))
| in(U_178,U_183)
| U_183 != set_meet(U_187)
| U_187 = empty_set ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_11,plain,
( in(sK36(U_187,U_184),U_173)
| ~ in(U_173,U_187)
| in(sK34(U_187,U_184),U_184)
| U_184 = set_meet(U_187)
| U_187 = empty_set ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_12,plain,
( ~ in(sK36(U_187,U_184),U_184)
| in(sK34(U_187,U_184),U_184)
| U_184 = set_meet(U_187)
| U_187 = empty_set ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_13,plain,
( in(sK35(U_187,U_184),U_187)
| in(sK36(U_187,U_184),U_173)
| ~ in(U_173,U_187)
| U_184 = set_meet(U_187)
| U_187 = empty_set ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_14,plain,
( ~ in(sK34(U_187,U_184),sK35(U_187,U_184))
| in(sK36(U_187,U_184),U_173)
| ~ in(U_173,U_187)
| U_184 = set_meet(U_187)
| U_187 = empty_set ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_15,plain,
( in(sK35(U_187,U_184),U_187)
| ~ in(sK36(U_187,U_184),U_184)
| U_184 = set_meet(U_187)
| U_187 = empty_set ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_16,plain,
( ~ in(sK34(U_187,U_184),sK35(U_187,U_184))
| ~ in(sK36(U_187,U_184),U_184)
| U_184 = set_meet(U_187)
| U_187 = empty_set ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_17,plain,
( U_185 = empty_set
| U_185 != set_meet(U_188)
| U_188 != empty_set ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_18,plain,
( U_186 = set_meet(U_188)
| U_186 != empty_set
| U_188 != empty_set ),
inference(clausify,[status(thm)],[f_28_7]) ).
fof(f_29_1,plain,
! [A,B] :
( ( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
& C = A )
| ( C != A
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| C != A )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(fof_nnf,[status(thm)],[d1_tarski]) ).
fof(f_29_2,plain,
! [U_192,U_191] :
( ( U_191 = singleton(U_192)
| ? [U_190] :
( ( ~ in(U_190,U_191)
& U_190 = U_192 )
| ( U_190 != U_192
& in(U_190,U_191) ) ) )
& ( ! [U_189] :
( ( in(U_189,U_191)
| U_189 != U_192 )
& ( U_189 = U_192
| ~ in(U_189,U_191) ) )
| U_191 != singleton(U_192) ) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
( ! [U_200,U_198] :
( U_198 = singleton(U_200)
| ? [U_196] :
( ~ in(U_196,U_198)
& U_196 = U_200 )
| ? [U_195] :
( U_195 != U_200
& in(U_195,U_198) ) )
& ! [U_199,U_197] :
( ( ! [U_194] :
( in(U_194,U_197)
| U_194 != U_199 )
& ! [U_193] :
( U_193 = U_199
| ~ in(U_193,U_197) ) )
| U_197 != singleton(U_199) ) ),
inference(miniscope,[status(thm)],[f_29_2]) ).
fof(f_29_4,plain,
( ! [U_200,U_198] :
( U_198 = singleton(U_200)
| ? [U_196] :
( ~ in(U_196,U_198)
& U_196 = U_200 )
| ( sK37(U_200,U_198) != U_200
& in(sK37(U_200,U_198),U_198) ) )
& ! [U_199,U_197] :
( ( ! [U_194] :
( in(U_194,U_197)
| U_194 != U_199 )
& ! [U_193] :
( U_193 = U_199
| ~ in(U_193,U_197) ) )
| U_197 != singleton(U_199) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_195,sK37(U_200,U_198))],[f_29_3]) ).
fof(f_29_5,plain,
( ! [U_200,U_198] :
( U_198 = singleton(U_200)
| ( ~ in(sK38(U_200,U_198),U_198)
& sK38(U_200,U_198) = U_200 )
| ( sK37(U_200,U_198) != U_200
& in(sK37(U_200,U_198),U_198) ) )
& ! [U_199,U_197] :
( ( ! [U_194] :
( in(U_194,U_197)
| U_194 != U_199 )
& ! [U_193] :
( U_193 = U_199
| ~ in(U_193,U_197) ) )
| U_197 != singleton(U_199) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_196,sK38(U_200,U_198))],[f_29_4]) ).
cnf(f_29_6,plain,
( U_193 = U_199
| ~ in(U_193,U_197)
| U_197 != singleton(U_199) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_7,plain,
( in(U_194,U_197)
| U_194 != U_199
| U_197 != singleton(U_199) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_8,plain,
( sK38(U_200,U_198) = U_200
| in(sK37(U_200,U_198),U_198)
| U_198 = singleton(U_200) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_9,plain,
( ~ in(sK38(U_200,U_198),U_198)
| in(sK37(U_200,U_198),U_198)
| U_198 = singleton(U_200) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_10,plain,
( sK38(U_200,U_198) = U_200
| sK37(U_200,U_198) != U_200
| U_198 = singleton(U_200) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_11,plain,
( ~ in(sK38(U_200,U_198),U_198)
| sK37(U_200,U_198) != U_200
| U_198 = singleton(U_200) ),
inference(clausify,[status(thm)],[f_29_5]) ).
fof(f_30_1,plain,
! [A] :
( ( A = empty_set
| ? [B] : in(B,A) )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(fof_nnf,[status(thm)],[d1_xboole_0]) ).
fof(f_30_2,plain,
! [U_203] :
( ( U_203 = empty_set
| ? [U_202] : in(U_202,U_203) )
& ( ! [U_201] : ~ in(U_201,U_203)
| U_203 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( ! [U_205] :
( U_205 = empty_set
| ? [U_202] : in(U_202,U_205) )
& ! [U_204] :
( ! [U_201] : ~ in(U_201,U_204)
| U_204 != empty_set ) ),
inference(miniscope,[status(thm)],[f_30_2]) ).
fof(f_30_4,plain,
( ! [U_205] :
( U_205 = empty_set
| in(sK39(U_205),U_205) )
& ! [U_204] :
( ! [U_201] : ~ in(U_201,U_204)
| U_204 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_202,sK39(U_205))],[f_30_3]) ).
cnf(f_30_5,plain,
( ~ in(U_201,U_204)
| U_204 != empty_set ),
inference(clausify,[status(thm)],[f_30_4]) ).
cnf(f_30_6,plain,
( U_205 = empty_set
| in(sK39(U_205),U_205) ),
inference(clausify,[status(thm)],[f_30_4]) ).
fof(f_31_1,plain,
! [A,B] :
( ( B = powerset(A)
| ? [C] :
( ( ~ in(C,B)
& subset(C,A) )
| ( ~ subset(C,A)
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ~ subset(C,A) )
& ( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(fof_nnf,[status(thm)],[d1_zfmisc_1]) ).
fof(f_31_2,plain,
! [U_209,U_208] :
( ( U_208 = powerset(U_209)
| ? [U_207] :
( ( ~ in(U_207,U_208)
& subset(U_207,U_209) )
| ( ~ subset(U_207,U_209)
& in(U_207,U_208) ) ) )
& ( ! [U_206] :
( ( in(U_206,U_208)
| ~ subset(U_206,U_209) )
& ( subset(U_206,U_209)
| ~ in(U_206,U_208) ) )
| U_208 != powerset(U_209) ) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( ! [U_217,U_215] :
( U_215 = powerset(U_217)
| ? [U_213] :
( ~ in(U_213,U_215)
& subset(U_213,U_217) )
| ? [U_212] :
( ~ subset(U_212,U_217)
& in(U_212,U_215) ) )
& ! [U_216,U_214] :
( ( ! [U_211] :
( in(U_211,U_214)
| ~ subset(U_211,U_216) )
& ! [U_210] :
( subset(U_210,U_216)
| ~ in(U_210,U_214) ) )
| U_214 != powerset(U_216) ) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
fof(f_31_4,plain,
( ! [U_217,U_215] :
( U_215 = powerset(U_217)
| ? [U_213] :
( ~ in(U_213,U_215)
& subset(U_213,U_217) )
| ( ~ subset(sK40(U_217,U_215),U_217)
& in(sK40(U_217,U_215),U_215) ) )
& ! [U_216,U_214] :
( ( ! [U_211] :
( in(U_211,U_214)
| ~ subset(U_211,U_216) )
& ! [U_210] :
( subset(U_210,U_216)
| ~ in(U_210,U_214) ) )
| U_214 != powerset(U_216) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_212,sK40(U_217,U_215))],[f_31_3]) ).
fof(f_31_5,plain,
( ! [U_217,U_215] :
( U_215 = powerset(U_217)
| ( ~ in(sK41(U_217,U_215),U_215)
& subset(sK41(U_217,U_215),U_217) )
| ( ~ subset(sK40(U_217,U_215),U_217)
& in(sK40(U_217,U_215),U_215) ) )
& ! [U_216,U_214] :
( ( ! [U_211] :
( in(U_211,U_214)
| ~ subset(U_211,U_216) )
& ! [U_210] :
( subset(U_210,U_216)
| ~ in(U_210,U_214) ) )
| U_214 != powerset(U_216) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_213,sK41(U_217,U_215))],[f_31_4]) ).
cnf(f_31_6,plain,
( subset(U_210,U_216)
| ~ in(U_210,U_214)
| U_214 != powerset(U_216) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_7,plain,
( in(U_211,U_214)
| ~ subset(U_211,U_216)
| U_214 != powerset(U_216) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_8,plain,
( subset(sK41(U_217,U_215),U_217)
| in(sK40(U_217,U_215),U_215)
| U_215 = powerset(U_217) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_9,plain,
( ~ in(sK41(U_217,U_215),U_215)
| in(sK40(U_217,U_215),U_215)
| U_215 = powerset(U_217) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_10,plain,
( subset(sK41(U_217,U_215),U_217)
| ~ subset(sK40(U_217,U_215),U_217)
| U_215 = powerset(U_217) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_11,plain,
( ~ in(sK41(U_217,U_215),U_215)
| ~ subset(sK40(U_217,U_215),U_217)
| U_215 = powerset(U_217) ),
inference(clausify,[status(thm)],[f_31_5]) ).
fof(f_32_1,plain,
! [A] :
( ( epsilon_transitive(A)
| ? [B] :
( ~ subset(B,A)
& in(B,A) ) )
& ( ! [B] :
( subset(B,A)
| ~ in(B,A) )
| ~ epsilon_transitive(A) ) ),
inference(fof_nnf,[status(thm)],[d2_ordinal1]) ).
fof(f_32_2,plain,
! [U_220] :
( ( epsilon_transitive(U_220)
| ? [U_219] :
( ~ subset(U_219,U_220)
& in(U_219,U_220) ) )
& ( ! [U_218] :
( subset(U_218,U_220)
| ~ in(U_218,U_220) )
| ~ epsilon_transitive(U_220) ) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
( ! [U_222] :
( epsilon_transitive(U_222)
| ? [U_219] :
( ~ subset(U_219,U_222)
& in(U_219,U_222) ) )
& ! [U_221] :
( ! [U_218] :
( subset(U_218,U_221)
| ~ in(U_218,U_221) )
| ~ epsilon_transitive(U_221) ) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
fof(f_32_4,plain,
( ! [U_222] :
( epsilon_transitive(U_222)
| ( ~ subset(sK42(U_222),U_222)
& in(sK42(U_222),U_222) ) )
& ! [U_221] :
( ! [U_218] :
( subset(U_218,U_221)
| ~ in(U_218,U_221) )
| ~ epsilon_transitive(U_221) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_219,sK42(U_222))],[f_32_3]) ).
cnf(f_32_5,plain,
( subset(U_218,U_221)
| ~ in(U_218,U_221)
| ~ epsilon_transitive(U_221) ),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_6,plain,
( in(sK42(U_222),U_222)
| epsilon_transitive(U_222) ),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_7,plain,
( ~ subset(sK42(U_222),U_222)
| epsilon_transitive(U_222) ),
inference(clausify,[status(thm)],[f_32_4]) ).
fof(f_33_1,plain,
! [A] :
( ! [B] :
( ( ( A = B
| ? [C,D] :
( ( ~ in(ordered_pair(C,D),A)
& in(ordered_pair(C,D),B) )
| ( ~ in(ordered_pair(C,D),B)
& in(ordered_pair(C,D),A) ) ) )
& ( ! [C,D] :
( ( in(ordered_pair(C,D),A)
| ~ in(ordered_pair(C,D),B) )
& ( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) ) )
| A != B ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d2_relat_1]) ).
fof(f_33_2,plain,
! [U_228] :
( ! [U_227] :
( ( ( U_228 = U_227
| ? [U_226,U_225] :
( ( ~ in(ordered_pair(U_226,U_225),U_228)
& in(ordered_pair(U_226,U_225),U_227) )
| ( ~ in(ordered_pair(U_226,U_225),U_227)
& in(ordered_pair(U_226,U_225),U_228) ) ) )
& ( ! [U_224,U_223] :
( ( in(ordered_pair(U_224,U_223),U_228)
| ~ in(ordered_pair(U_224,U_223),U_227) )
& ( in(ordered_pair(U_224,U_223),U_227)
| ~ in(ordered_pair(U_224,U_223),U_228) ) )
| U_228 != U_227 ) )
| ~ relation(U_227) )
| ~ relation(U_228) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_228] :
( ! [U_227] :
( ( ( U_228 = U_227
| ? [U_236,U_234] :
( ~ in(ordered_pair(U_236,U_234),U_228)
& in(ordered_pair(U_236,U_234),U_227) )
| ? [U_235,U_233] :
( ~ in(ordered_pair(U_235,U_233),U_227)
& in(ordered_pair(U_235,U_233),U_228) ) )
& ( ( ! [U_232,U_230] :
( in(ordered_pair(U_232,U_230),U_228)
| ~ in(ordered_pair(U_232,U_230),U_227) )
& ! [U_231,U_229] :
( in(ordered_pair(U_231,U_229),U_227)
| ~ in(ordered_pair(U_231,U_229),U_228) ) )
| U_228 != U_227 ) )
| ~ relation(U_227) )
| ~ relation(U_228) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
fof(f_33_4,plain,
! [U_228] :
( ! [U_227] :
( ( ( U_228 = U_227
| ? [U_236,U_234] :
( ~ in(ordered_pair(U_236,U_234),U_228)
& in(ordered_pair(U_236,U_234),U_227) )
| ? [U_233] :
( ~ in(ordered_pair(sK43(U_228,U_227),U_233),U_227)
& in(ordered_pair(sK43(U_228,U_227),U_233),U_228) ) )
& ( ( ! [U_232,U_230] :
( in(ordered_pair(U_232,U_230),U_228)
| ~ in(ordered_pair(U_232,U_230),U_227) )
& ! [U_231,U_229] :
( in(ordered_pair(U_231,U_229),U_227)
| ~ in(ordered_pair(U_231,U_229),U_228) ) )
| U_228 != U_227 ) )
| ~ relation(U_227) )
| ~ relation(U_228) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_235,sK43(U_228,U_227))],[f_33_3]) ).
fof(f_33_5,plain,
! [U_228] :
( ! [U_227] :
( ( ( U_228 = U_227
| ? [U_236,U_234] :
( ~ in(ordered_pair(U_236,U_234),U_228)
& in(ordered_pair(U_236,U_234),U_227) )
| ( ~ in(ordered_pair(sK43(U_228,U_227),sK44(U_228,U_227)),U_227)
& in(ordered_pair(sK43(U_228,U_227),sK44(U_228,U_227)),U_228) ) )
& ( ( ! [U_232,U_230] :
( in(ordered_pair(U_232,U_230),U_228)
| ~ in(ordered_pair(U_232,U_230),U_227) )
& ! [U_231,U_229] :
( in(ordered_pair(U_231,U_229),U_227)
| ~ in(ordered_pair(U_231,U_229),U_228) ) )
| U_228 != U_227 ) )
| ~ relation(U_227) )
| ~ relation(U_228) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_233,sK44(U_228,U_227))],[f_33_4]) ).
fof(f_33_6,plain,
! [U_228] :
( ! [U_227] :
( ( ( U_228 = U_227
| ? [U_234] :
( ~ in(ordered_pair(sK45(U_228,U_227),U_234),U_228)
& in(ordered_pair(sK45(U_228,U_227),U_234),U_227) )
| ( ~ in(ordered_pair(sK43(U_228,U_227),sK44(U_228,U_227)),U_227)
& in(ordered_pair(sK43(U_228,U_227),sK44(U_228,U_227)),U_228) ) )
& ( ( ! [U_232,U_230] :
( in(ordered_pair(U_232,U_230),U_228)
| ~ in(ordered_pair(U_232,U_230),U_227) )
& ! [U_231,U_229] :
( in(ordered_pair(U_231,U_229),U_227)
| ~ in(ordered_pair(U_231,U_229),U_228) ) )
| U_228 != U_227 ) )
| ~ relation(U_227) )
| ~ relation(U_228) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_236,sK45(U_228,U_227))],[f_33_5]) ).
fof(f_33_7,plain,
! [U_228] :
( ! [U_227] :
( ( ( U_228 = U_227
| ( ~ in(ordered_pair(sK45(U_228,U_227),sK46(U_228,U_227)),U_228)
& in(ordered_pair(sK45(U_228,U_227),sK46(U_228,U_227)),U_227) )
| ( ~ in(ordered_pair(sK43(U_228,U_227),sK44(U_228,U_227)),U_227)
& in(ordered_pair(sK43(U_228,U_227),sK44(U_228,U_227)),U_228) ) )
& ( ( ! [U_232,U_230] :
( in(ordered_pair(U_232,U_230),U_228)
| ~ in(ordered_pair(U_232,U_230),U_227) )
& ! [U_231,U_229] :
( in(ordered_pair(U_231,U_229),U_227)
| ~ in(ordered_pair(U_231,U_229),U_228) ) )
| U_228 != U_227 ) )
| ~ relation(U_227) )
| ~ relation(U_228) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_234,sK46(U_228,U_227))],[f_33_6]) ).
cnf(f_33_8,plain,
( in(ordered_pair(U_231,U_229),U_227)
| ~ in(ordered_pair(U_231,U_229),U_228)
| U_228 != U_227
| ~ relation(U_227)
| ~ relation(U_228) ),
inference(clausify,[status(thm)],[f_33_7]) ).
cnf(f_33_9,plain,
( in(ordered_pair(U_232,U_230),U_228)
| ~ in(ordered_pair(U_232,U_230),U_227)
| U_228 != U_227
| ~ relation(U_227)
| ~ relation(U_228) ),
inference(clausify,[status(thm)],[f_33_7]) ).
cnf(f_33_10,plain,
( in(ordered_pair(sK45(U_228,U_227),sK46(U_228,U_227)),U_227)
| in(ordered_pair(sK43(U_228,U_227),sK44(U_228,U_227)),U_228)
| U_228 = U_227
| ~ relation(U_227)
| ~ relation(U_228) ),
inference(clausify,[status(thm)],[f_33_7]) ).
cnf(f_33_11,plain,
( ~ in(ordered_pair(sK45(U_228,U_227),sK46(U_228,U_227)),U_228)
| in(ordered_pair(sK43(U_228,U_227),sK44(U_228,U_227)),U_228)
| U_228 = U_227
| ~ relation(U_227)
| ~ relation(U_228) ),
inference(clausify,[status(thm)],[f_33_7]) ).
cnf(f_33_12,plain,
( in(ordered_pair(sK45(U_228,U_227),sK46(U_228,U_227)),U_227)
| ~ in(ordered_pair(sK43(U_228,U_227),sK44(U_228,U_227)),U_227)
| U_228 = U_227
| ~ relation(U_227)
| ~ relation(U_228) ),
inference(clausify,[status(thm)],[f_33_7]) ).
cnf(f_33_13,plain,
( ~ in(ordered_pair(sK45(U_228,U_227),sK46(U_228,U_227)),U_228)
| ~ in(ordered_pair(sK43(U_228,U_227),sK44(U_228,U_227)),U_227)
| U_228 = U_227
| ~ relation(U_227)
| ~ relation(U_228) ),
inference(clausify,[status(thm)],[f_33_7]) ).
fof(f_34_1,plain,
! [A,B] :
( ( ( ( element(B,A)
| ~ empty(B) )
& ( empty(B)
| ~ element(B,A) ) )
| ~ empty(A) )
& ( ( ( element(B,A)
| ~ in(B,A) )
& ( in(B,A)
| ~ element(B,A) ) )
| empty(A) ) ),
inference(fof_nnf,[status(thm)],[d2_subset_1]) ).
fof(f_34_2,plain,
! [U_238,U_237] :
( ( ( ( element(U_237,U_238)
| ~ empty(U_237) )
& ( empty(U_237)
| ~ element(U_237,U_238) ) )
| ~ empty(U_238) )
& ( ( ( element(U_237,U_238)
| ~ in(U_237,U_238) )
& ( in(U_237,U_238)
| ~ element(U_237,U_238) ) )
| empty(U_238) ) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
( ! [U_246] :
( ( ! [U_244] :
( element(U_244,U_246)
| ~ empty(U_244) )
& ! [U_243] :
( empty(U_243)
| ~ element(U_243,U_246) ) )
| ~ empty(U_246) )
& ! [U_245] :
( ( ! [U_242] :
( element(U_242,U_245)
| ~ in(U_242,U_245) )
& ! [U_241] :
( in(U_241,U_245)
| ~ element(U_241,U_245) ) )
| empty(U_245) ) ),
inference(miniscope,[status(thm)],[f_34_2]) ).
cnf(f_34_4,plain,
( in(U_241,U_245)
| ~ element(U_241,U_245)
| empty(U_245) ),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_5,plain,
( element(U_242,U_245)
| ~ in(U_242,U_245)
| empty(U_245) ),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_6,plain,
( empty(U_243)
| ~ element(U_243,U_246)
| ~ empty(U_246) ),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_7,plain,
( element(U_244,U_246)
| ~ empty(U_244)
| ~ empty(U_246) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
! [A,B,C] :
( ( C = unordered_pair(A,B)
| ? [D] :
( ( ~ in(D,C)
& ( D = B
| D = A ) )
| ( D != B
& D != A
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ( D != B
& D != A ) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(fof_nnf,[status(thm)],[d2_tarski]) ).
fof(f_35_2,plain,
! [U_251,U_250,U_249] :
( ( U_249 = unordered_pair(U_251,U_250)
| ? [U_248] :
( ( ~ in(U_248,U_249)
& ( U_248 = U_250
| U_248 = U_251 ) )
| ( U_248 != U_250
& U_248 != U_251
& in(U_248,U_249) ) ) )
& ( ! [U_247] :
( ( in(U_247,U_249)
| ( U_247 != U_250
& U_247 != U_251 ) )
& ( U_247 = U_250
| U_247 = U_251
| ~ in(U_247,U_249) ) )
| U_249 != unordered_pair(U_251,U_250) ) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( ! [U_261,U_259,U_257] :
( U_257 = unordered_pair(U_261,U_259)
| ? [U_255] :
( ~ in(U_255,U_257)
& ( U_255 = U_259
| U_255 = U_261 ) )
| ? [U_254] :
( U_254 != U_259
& U_254 != U_261
& in(U_254,U_257) ) )
& ! [U_260,U_258,U_256] :
( ( ! [U_253] :
( in(U_253,U_256)
| ( U_253 != U_258
& U_253 != U_260 ) )
& ! [U_252] :
( U_252 = U_258
| U_252 = U_260
| ~ in(U_252,U_256) ) )
| U_256 != unordered_pair(U_260,U_258) ) ),
inference(miniscope,[status(thm)],[f_35_2]) ).
fof(f_35_4,plain,
( ! [U_261,U_259,U_257] :
( U_257 = unordered_pair(U_261,U_259)
| ? [U_255] :
( ~ in(U_255,U_257)
& ( U_255 = U_259
| U_255 = U_261 ) )
| ( sK47(U_261,U_259,U_257) != U_259
& sK47(U_261,U_259,U_257) != U_261
& in(sK47(U_261,U_259,U_257),U_257) ) )
& ! [U_260,U_258,U_256] :
( ( ! [U_253] :
( in(U_253,U_256)
| ( U_253 != U_258
& U_253 != U_260 ) )
& ! [U_252] :
( U_252 = U_258
| U_252 = U_260
| ~ in(U_252,U_256) ) )
| U_256 != unordered_pair(U_260,U_258) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_254,sK47(U_261,U_259,U_257))],[f_35_3]) ).
fof(f_35_5,plain,
( ! [U_261,U_259,U_257] :
( U_257 = unordered_pair(U_261,U_259)
| ( ~ in(sK48(U_261,U_259,U_257),U_257)
& ( sK48(U_261,U_259,U_257) = U_259
| sK48(U_261,U_259,U_257) = U_261 ) )
| ( sK47(U_261,U_259,U_257) != U_259
& sK47(U_261,U_259,U_257) != U_261
& in(sK47(U_261,U_259,U_257),U_257) ) )
& ! [U_260,U_258,U_256] :
( ( ! [U_253] :
( in(U_253,U_256)
| ( U_253 != U_258
& U_253 != U_260 ) )
& ! [U_252] :
( U_252 = U_258
| U_252 = U_260
| ~ in(U_252,U_256) ) )
| U_256 != unordered_pair(U_260,U_258) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_255,sK48(U_261,U_259,U_257))],[f_35_4]) ).
cnf(f_35_6,plain,
( U_252 = U_258
| U_252 = U_260
| ~ in(U_252,U_256)
| U_256 != unordered_pair(U_260,U_258) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_7,plain,
( U_253 != U_260
| in(U_253,U_256)
| U_256 != unordered_pair(U_260,U_258) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_8,plain,
( U_253 != U_258
| in(U_253,U_256)
| U_256 != unordered_pair(U_260,U_258) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_9,plain,
( sK48(U_261,U_259,U_257) = U_259
| sK48(U_261,U_259,U_257) = U_261
| in(sK47(U_261,U_259,U_257),U_257)
| U_257 = unordered_pair(U_261,U_259) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_10,plain,
( ~ in(sK48(U_261,U_259,U_257),U_257)
| in(sK47(U_261,U_259,U_257),U_257)
| U_257 = unordered_pair(U_261,U_259) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_11,plain,
( sK47(U_261,U_259,U_257) != U_261
| sK48(U_261,U_259,U_257) = U_259
| sK48(U_261,U_259,U_257) = U_261
| U_257 = unordered_pair(U_261,U_259) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_12,plain,
( sK47(U_261,U_259,U_257) != U_259
| sK48(U_261,U_259,U_257) = U_259
| sK48(U_261,U_259,U_257) = U_261
| U_257 = unordered_pair(U_261,U_259) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_13,plain,
( sK47(U_261,U_259,U_257) != U_261
| ~ in(sK48(U_261,U_259,U_257),U_257)
| U_257 = unordered_pair(U_261,U_259) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_14,plain,
( sK47(U_261,U_259,U_257) != U_259
| ~ in(sK48(U_261,U_259,U_257),U_257)
| U_257 = unordered_pair(U_261,U_259) ),
inference(clausify,[status(thm)],[f_35_5]) ).
fof(f_36_1,plain,
! [A] :
( ( ( well_founded_relation(A)
| ? [B] :
( ! [C] :
( ~ disjoint(fiber(A,C),B)
| ~ in(C,B) )
& B != empty_set
& subset(B,relation_field(A)) ) )
& ( ! [B] :
( ? [C] :
( disjoint(fiber(A,C),B)
& in(C,B) )
| B = empty_set
| ~ subset(B,relation_field(A)) )
| ~ well_founded_relation(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d2_wellord1]) ).
fof(f_36_2,plain,
! [U_266] :
( ( ( well_founded_relation(U_266)
| ? [U_265] :
( ! [U_264] :
( ~ disjoint(fiber(U_266,U_264),U_265)
| ~ in(U_264,U_265) )
& U_265 != empty_set
& subset(U_265,relation_field(U_266)) ) )
& ( ! [U_263] :
( ? [U_262] :
( disjoint(fiber(U_266,U_262),U_263)
& in(U_262,U_263) )
| U_263 = empty_set
| ~ subset(U_263,relation_field(U_266)) )
| ~ well_founded_relation(U_266) ) )
| ~ relation(U_266) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_266] :
( ( ( well_founded_relation(U_266)
| ? [U_265] :
( ! [U_264] :
( ~ disjoint(fiber(U_266,U_264),U_265)
| ~ in(U_264,U_265) )
& U_265 != empty_set
& subset(U_265,relation_field(U_266)) ) )
& ( ! [U_263] :
( ( disjoint(fiber(U_266,sK49(U_266,U_263)),U_263)
& in(sK49(U_266,U_263),U_263) )
| U_263 = empty_set
| ~ subset(U_263,relation_field(U_266)) )
| ~ well_founded_relation(U_266) ) )
| ~ relation(U_266) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_262,sK49(U_266,U_263))],[f_36_2]) ).
fof(f_36_4,plain,
! [U_266] :
( ( ( well_founded_relation(U_266)
| ( ! [U_264] :
( ~ disjoint(fiber(U_266,U_264),sK50(U_266))
| ~ in(U_264,sK50(U_266)) )
& sK50(U_266) != empty_set
& subset(sK50(U_266),relation_field(U_266)) ) )
& ( ! [U_263] :
( ( disjoint(fiber(U_266,sK49(U_266,U_263)),U_263)
& in(sK49(U_266,U_263),U_263) )
| U_263 = empty_set
| ~ subset(U_263,relation_field(U_266)) )
| ~ well_founded_relation(U_266) ) )
| ~ relation(U_266) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_265,sK50(U_266))],[f_36_3]) ).
cnf(f_36_5,plain,
( in(sK49(U_266,U_263),U_263)
| U_263 = empty_set
| ~ subset(U_263,relation_field(U_266))
| ~ well_founded_relation(U_266)
| ~ relation(U_266) ),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_6,plain,
( disjoint(fiber(U_266,sK49(U_266,U_263)),U_263)
| U_263 = empty_set
| ~ subset(U_263,relation_field(U_266))
| ~ well_founded_relation(U_266)
| ~ relation(U_266) ),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_7,plain,
( subset(sK50(U_266),relation_field(U_266))
| well_founded_relation(U_266)
| ~ relation(U_266) ),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_8,plain,
( sK50(U_266) != empty_set
| well_founded_relation(U_266)
| ~ relation(U_266) ),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_9,plain,
( ~ disjoint(fiber(U_266,U_264),sK50(U_266))
| ~ in(U_264,sK50(U_266))
| well_founded_relation(U_266)
| ~ relation(U_266) ),
inference(clausify,[status(thm)],[f_36_4]) ).
fof(f_37_1,plain,
! [A,B,C] :
( ( C = set_union2(A,B)
| ? [D] :
( ( ~ in(D,C)
& ( in(D,B)
| in(D,A) ) )
| ( ~ in(D,B)
& ~ in(D,A)
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ( ~ in(D,B)
& ~ in(D,A) ) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(fof_nnf,[status(thm)],[d2_xboole_0]) ).
fof(f_37_2,plain,
! [U_271,U_270,U_269] :
( ( U_269 = set_union2(U_271,U_270)
| ? [U_268] :
( ( ~ in(U_268,U_269)
& ( in(U_268,U_270)
| in(U_268,U_271) ) )
| ( ~ in(U_268,U_270)
& ~ in(U_268,U_271)
& in(U_268,U_269) ) ) )
& ( ! [U_267] :
( ( in(U_267,U_269)
| ( ~ in(U_267,U_270)
& ~ in(U_267,U_271) ) )
& ( in(U_267,U_270)
| in(U_267,U_271)
| ~ in(U_267,U_269) ) )
| U_269 != set_union2(U_271,U_270) ) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
( ! [U_281,U_279,U_277] :
( U_277 = set_union2(U_281,U_279)
| ? [U_275] :
( ~ in(U_275,U_277)
& ( in(U_275,U_279)
| in(U_275,U_281) ) )
| ? [U_274] :
( ~ in(U_274,U_279)
& ~ in(U_274,U_281)
& in(U_274,U_277) ) )
& ! [U_280,U_278,U_276] :
( ( ! [U_273] :
( in(U_273,U_276)
| ( ~ in(U_273,U_278)
& ~ in(U_273,U_280) ) )
& ! [U_272] :
( in(U_272,U_278)
| in(U_272,U_280)
| ~ in(U_272,U_276) ) )
| U_276 != set_union2(U_280,U_278) ) ),
inference(miniscope,[status(thm)],[f_37_2]) ).
fof(f_37_4,plain,
( ! [U_281,U_279,U_277] :
( U_277 = set_union2(U_281,U_279)
| ? [U_275] :
( ~ in(U_275,U_277)
& ( in(U_275,U_279)
| in(U_275,U_281) ) )
| ( ~ in(sK51(U_281,U_279,U_277),U_279)
& ~ in(sK51(U_281,U_279,U_277),U_281)
& in(sK51(U_281,U_279,U_277),U_277) ) )
& ! [U_280,U_278,U_276] :
( ( ! [U_273] :
( in(U_273,U_276)
| ( ~ in(U_273,U_278)
& ~ in(U_273,U_280) ) )
& ! [U_272] :
( in(U_272,U_278)
| in(U_272,U_280)
| ~ in(U_272,U_276) ) )
| U_276 != set_union2(U_280,U_278) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_274,sK51(U_281,U_279,U_277))],[f_37_3]) ).
fof(f_37_5,plain,
( ! [U_281,U_279,U_277] :
( U_277 = set_union2(U_281,U_279)
| ( ~ in(sK52(U_281,U_279,U_277),U_277)
& ( in(sK52(U_281,U_279,U_277),U_279)
| in(sK52(U_281,U_279,U_277),U_281) ) )
| ( ~ in(sK51(U_281,U_279,U_277),U_279)
& ~ in(sK51(U_281,U_279,U_277),U_281)
& in(sK51(U_281,U_279,U_277),U_277) ) )
& ! [U_280,U_278,U_276] :
( ( ! [U_273] :
( in(U_273,U_276)
| ( ~ in(U_273,U_278)
& ~ in(U_273,U_280) ) )
& ! [U_272] :
( in(U_272,U_278)
| in(U_272,U_280)
| ~ in(U_272,U_276) ) )
| U_276 != set_union2(U_280,U_278) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_275,sK52(U_281,U_279,U_277))],[f_37_4]) ).
cnf(f_37_6,plain,
( in(U_272,U_278)
| in(U_272,U_280)
| ~ in(U_272,U_276)
| U_276 != set_union2(U_280,U_278) ),
inference(clausify,[status(thm)],[f_37_5]) ).
cnf(f_37_7,plain,
( ~ in(U_273,U_280)
| in(U_273,U_276)
| U_276 != set_union2(U_280,U_278) ),
inference(clausify,[status(thm)],[f_37_5]) ).
cnf(f_37_8,plain,
( ~ in(U_273,U_278)
| in(U_273,U_276)
| U_276 != set_union2(U_280,U_278) ),
inference(clausify,[status(thm)],[f_37_5]) ).
cnf(f_37_9,plain,
( in(sK52(U_281,U_279,U_277),U_279)
| in(sK52(U_281,U_279,U_277),U_281)
| in(sK51(U_281,U_279,U_277),U_277)
| U_277 = set_union2(U_281,U_279) ),
inference(clausify,[status(thm)],[f_37_5]) ).
cnf(f_37_10,plain,
( ~ in(sK52(U_281,U_279,U_277),U_277)
| in(sK51(U_281,U_279,U_277),U_277)
| U_277 = set_union2(U_281,U_279) ),
inference(clausify,[status(thm)],[f_37_5]) ).
cnf(f_37_11,plain,
( ~ in(sK51(U_281,U_279,U_277),U_281)
| in(sK52(U_281,U_279,U_277),U_279)
| in(sK52(U_281,U_279,U_277),U_281)
| U_277 = set_union2(U_281,U_279) ),
inference(clausify,[status(thm)],[f_37_5]) ).
cnf(f_37_12,plain,
( ~ in(sK51(U_281,U_279,U_277),U_279)
| in(sK52(U_281,U_279,U_277),U_279)
| in(sK52(U_281,U_279,U_277),U_281)
| U_277 = set_union2(U_281,U_279) ),
inference(clausify,[status(thm)],[f_37_5]) ).
cnf(f_37_13,plain,
( ~ in(sK51(U_281,U_279,U_277),U_281)
| ~ in(sK52(U_281,U_279,U_277),U_277)
| U_277 = set_union2(U_281,U_279) ),
inference(clausify,[status(thm)],[f_37_5]) ).
cnf(f_37_14,plain,
( ~ in(sK51(U_281,U_279,U_277),U_279)
| ~ in(sK52(U_281,U_279,U_277),U_277)
| U_277 = set_union2(U_281,U_279) ),
inference(clausify,[status(thm)],[f_37_5]) ).
fof(f_38_1,plain,
! [A,B,C] :
( ( C = cartesian_product2(A,B)
| ? [D] :
( ( ~ in(D,C)
& ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) ) )
| ( ! [E,F] :
( D != ordered_pair(E,F)
| ~ in(F,B)
| ~ in(E,A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ! [E,F] :
( D != ordered_pair(E,F)
| ~ in(F,B)
| ~ in(E,A) ) )
& ( ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) )
| ~ in(D,C) ) )
| C != cartesian_product2(A,B) ) ),
inference(fof_nnf,[status(thm)],[d2_zfmisc_1]) ).
fof(f_38_2,plain,
! [U_294,U_293,U_292] :
( ( U_292 = cartesian_product2(U_294,U_293)
| ? [U_291] :
( ( ~ in(U_291,U_292)
& ? [U_290,U_289] :
( U_291 = ordered_pair(U_290,U_289)
& in(U_289,U_293)
& in(U_290,U_294) ) )
| ( ! [U_288,U_287] :
( U_291 != ordered_pair(U_288,U_287)
| ~ in(U_287,U_293)
| ~ in(U_288,U_294) )
& in(U_291,U_292) ) ) )
& ( ! [U_286] :
( ( in(U_286,U_292)
| ! [U_285,U_284] :
( U_286 != ordered_pair(U_285,U_284)
| ~ in(U_284,U_293)
| ~ in(U_285,U_294) ) )
& ( ? [U_283,U_282] :
( U_286 = ordered_pair(U_283,U_282)
& in(U_282,U_293)
& in(U_283,U_294) )
| ~ in(U_286,U_292) ) )
| U_292 != cartesian_product2(U_294,U_293) ) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
( ! [U_304,U_302,U_300] :
( U_300 = cartesian_product2(U_304,U_302)
| ? [U_298] :
( ~ in(U_298,U_300)
& ? [U_290] :
( ? [U_289] :
( U_298 = ordered_pair(U_290,U_289)
& in(U_289,U_302) )
& in(U_290,U_304) ) )
| ? [U_297] :
( ! [U_288] :
( ! [U_287] :
( U_297 != ordered_pair(U_288,U_287)
| ~ in(U_287,U_302) )
| ~ in(U_288,U_304) )
& in(U_297,U_300) ) )
& ! [U_303,U_301,U_299] :
( ( ! [U_296] :
( in(U_296,U_299)
| ! [U_285] :
( ! [U_284] :
( U_296 != ordered_pair(U_285,U_284)
| ~ in(U_284,U_301) )
| ~ in(U_285,U_303) ) )
& ! [U_295] :
( ? [U_283] :
( ? [U_282] :
( U_295 = ordered_pair(U_283,U_282)
& in(U_282,U_301) )
& in(U_283,U_303) )
| ~ in(U_295,U_299) ) )
| U_299 != cartesian_product2(U_303,U_301) ) ),
inference(miniscope,[status(thm)],[f_38_2]) ).
fof(f_38_4,plain,
( ! [U_304,U_302,U_300] :
( U_300 = cartesian_product2(U_304,U_302)
| ? [U_298] :
( ~ in(U_298,U_300)
& ? [U_290] :
( ? [U_289] :
( U_298 = ordered_pair(U_290,U_289)
& in(U_289,U_302) )
& in(U_290,U_304) ) )
| ? [U_297] :
( ! [U_288] :
( ! [U_287] :
( U_297 != ordered_pair(U_288,U_287)
| ~ in(U_287,U_302) )
| ~ in(U_288,U_304) )
& in(U_297,U_300) ) )
& ! [U_303,U_301,U_299] :
( ( ! [U_296] :
( in(U_296,U_299)
| ! [U_285] :
( ! [U_284] :
( U_296 != ordered_pair(U_285,U_284)
| ~ in(U_284,U_301) )
| ~ in(U_285,U_303) ) )
& ! [U_295] :
( ( ? [U_282] :
( U_295 = ordered_pair(sK53(U_303,U_301,U_299,U_295),U_282)
& in(U_282,U_301) )
& in(sK53(U_303,U_301,U_299,U_295),U_303) )
| ~ in(U_295,U_299) ) )
| U_299 != cartesian_product2(U_303,U_301) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_283,sK53(U_303,U_301,U_299,U_295))],[f_38_3]) ).
fof(f_38_5,plain,
( ! [U_304,U_302,U_300] :
( U_300 = cartesian_product2(U_304,U_302)
| ? [U_298] :
( ~ in(U_298,U_300)
& ? [U_290] :
( ? [U_289] :
( U_298 = ordered_pair(U_290,U_289)
& in(U_289,U_302) )
& in(U_290,U_304) ) )
| ? [U_297] :
( ! [U_288] :
( ! [U_287] :
( U_297 != ordered_pair(U_288,U_287)
| ~ in(U_287,U_302) )
| ~ in(U_288,U_304) )
& in(U_297,U_300) ) )
& ! [U_303,U_301,U_299] :
( ( ! [U_296] :
( in(U_296,U_299)
| ! [U_285] :
( ! [U_284] :
( U_296 != ordered_pair(U_285,U_284)
| ~ in(U_284,U_301) )
| ~ in(U_285,U_303) ) )
& ! [U_295] :
( ( U_295 = ordered_pair(sK53(U_303,U_301,U_299,U_295),sK54(U_303,U_301,U_299,U_295))
& in(sK54(U_303,U_301,U_299,U_295),U_301)
& in(sK53(U_303,U_301,U_299,U_295),U_303) )
| ~ in(U_295,U_299) ) )
| U_299 != cartesian_product2(U_303,U_301) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_282,sK54(U_303,U_301,U_299,U_295))],[f_38_4]) ).
fof(f_38_6,plain,
( ! [U_304,U_302,U_300] :
( U_300 = cartesian_product2(U_304,U_302)
| ? [U_298] :
( ~ in(U_298,U_300)
& ? [U_290] :
( ? [U_289] :
( U_298 = ordered_pair(U_290,U_289)
& in(U_289,U_302) )
& in(U_290,U_304) ) )
| ( ! [U_288] :
( ! [U_287] :
( sK55(U_304,U_302,U_300) != ordered_pair(U_288,U_287)
| ~ in(U_287,U_302) )
| ~ in(U_288,U_304) )
& in(sK55(U_304,U_302,U_300),U_300) ) )
& ! [U_303,U_301,U_299] :
( ( ! [U_296] :
( in(U_296,U_299)
| ! [U_285] :
( ! [U_284] :
( U_296 != ordered_pair(U_285,U_284)
| ~ in(U_284,U_301) )
| ~ in(U_285,U_303) ) )
& ! [U_295] :
( ( U_295 = ordered_pair(sK53(U_303,U_301,U_299,U_295),sK54(U_303,U_301,U_299,U_295))
& in(sK54(U_303,U_301,U_299,U_295),U_301)
& in(sK53(U_303,U_301,U_299,U_295),U_303) )
| ~ in(U_295,U_299) ) )
| U_299 != cartesian_product2(U_303,U_301) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_297,sK55(U_304,U_302,U_300))],[f_38_5]) ).
fof(f_38_7,plain,
( ! [U_304,U_302,U_300] :
( U_300 = cartesian_product2(U_304,U_302)
| ( ~ in(sK56(U_304,U_302,U_300),U_300)
& ? [U_290] :
( ? [U_289] :
( sK56(U_304,U_302,U_300) = ordered_pair(U_290,U_289)
& in(U_289,U_302) )
& in(U_290,U_304) ) )
| ( ! [U_288] :
( ! [U_287] :
( sK55(U_304,U_302,U_300) != ordered_pair(U_288,U_287)
| ~ in(U_287,U_302) )
| ~ in(U_288,U_304) )
& in(sK55(U_304,U_302,U_300),U_300) ) )
& ! [U_303,U_301,U_299] :
( ( ! [U_296] :
( in(U_296,U_299)
| ! [U_285] :
( ! [U_284] :
( U_296 != ordered_pair(U_285,U_284)
| ~ in(U_284,U_301) )
| ~ in(U_285,U_303) ) )
& ! [U_295] :
( ( U_295 = ordered_pair(sK53(U_303,U_301,U_299,U_295),sK54(U_303,U_301,U_299,U_295))
& in(sK54(U_303,U_301,U_299,U_295),U_301)
& in(sK53(U_303,U_301,U_299,U_295),U_303) )
| ~ in(U_295,U_299) ) )
| U_299 != cartesian_product2(U_303,U_301) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_298,sK56(U_304,U_302,U_300))],[f_38_6]) ).
fof(f_38_8,plain,
( ! [U_304,U_302,U_300] :
( U_300 = cartesian_product2(U_304,U_302)
| ( ~ in(sK56(U_304,U_302,U_300),U_300)
& ? [U_289] :
( sK56(U_304,U_302,U_300) = ordered_pair(sK57(U_304,U_302,U_300),U_289)
& in(U_289,U_302) )
& in(sK57(U_304,U_302,U_300),U_304) )
| ( ! [U_288] :
( ! [U_287] :
( sK55(U_304,U_302,U_300) != ordered_pair(U_288,U_287)
| ~ in(U_287,U_302) )
| ~ in(U_288,U_304) )
& in(sK55(U_304,U_302,U_300),U_300) ) )
& ! [U_303,U_301,U_299] :
( ( ! [U_296] :
( in(U_296,U_299)
| ! [U_285] :
( ! [U_284] :
( U_296 != ordered_pair(U_285,U_284)
| ~ in(U_284,U_301) )
| ~ in(U_285,U_303) ) )
& ! [U_295] :
( ( U_295 = ordered_pair(sK53(U_303,U_301,U_299,U_295),sK54(U_303,U_301,U_299,U_295))
& in(sK54(U_303,U_301,U_299,U_295),U_301)
& in(sK53(U_303,U_301,U_299,U_295),U_303) )
| ~ in(U_295,U_299) ) )
| U_299 != cartesian_product2(U_303,U_301) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_290,sK57(U_304,U_302,U_300))],[f_38_7]) ).
fof(f_38_9,plain,
( ! [U_304,U_302,U_300] :
( U_300 = cartesian_product2(U_304,U_302)
| ( ~ in(sK56(U_304,U_302,U_300),U_300)
& sK56(U_304,U_302,U_300) = ordered_pair(sK57(U_304,U_302,U_300),sK58(U_304,U_302,U_300))
& in(sK58(U_304,U_302,U_300),U_302)
& in(sK57(U_304,U_302,U_300),U_304) )
| ( ! [U_288] :
( ! [U_287] :
( sK55(U_304,U_302,U_300) != ordered_pair(U_288,U_287)
| ~ in(U_287,U_302) )
| ~ in(U_288,U_304) )
& in(sK55(U_304,U_302,U_300),U_300) ) )
& ! [U_303,U_301,U_299] :
( ( ! [U_296] :
( in(U_296,U_299)
| ! [U_285] :
( ! [U_284] :
( U_296 != ordered_pair(U_285,U_284)
| ~ in(U_284,U_301) )
| ~ in(U_285,U_303) ) )
& ! [U_295] :
( ( U_295 = ordered_pair(sK53(U_303,U_301,U_299,U_295),sK54(U_303,U_301,U_299,U_295))
& in(sK54(U_303,U_301,U_299,U_295),U_301)
& in(sK53(U_303,U_301,U_299,U_295),U_303) )
| ~ in(U_295,U_299) ) )
| U_299 != cartesian_product2(U_303,U_301) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_289,sK58(U_304,U_302,U_300))],[f_38_8]) ).
cnf(f_38_10,plain,
( in(sK53(U_303,U_301,U_299,U_295),U_303)
| ~ in(U_295,U_299)
| U_299 != cartesian_product2(U_303,U_301) ),
inference(clausify,[status(thm)],[f_38_9]) ).
cnf(f_38_11,plain,
( in(sK54(U_303,U_301,U_299,U_295),U_301)
| ~ in(U_295,U_299)
| U_299 != cartesian_product2(U_303,U_301) ),
inference(clausify,[status(thm)],[f_38_9]) ).
cnf(f_38_12,plain,
( U_295 = ordered_pair(sK53(U_303,U_301,U_299,U_295),sK54(U_303,U_301,U_299,U_295))
| ~ in(U_295,U_299)
| U_299 != cartesian_product2(U_303,U_301) ),
inference(clausify,[status(thm)],[f_38_9]) ).
cnf(f_38_13,plain,
( in(U_296,U_299)
| U_296 != ordered_pair(U_285,U_284)
| ~ in(U_284,U_301)
| ~ in(U_285,U_303)
| U_299 != cartesian_product2(U_303,U_301) ),
inference(clausify,[status(thm)],[f_38_9]) ).
cnf(f_38_14,plain,
( in(sK57(U_304,U_302,U_300),U_304)
| in(sK55(U_304,U_302,U_300),U_300)
| U_300 = cartesian_product2(U_304,U_302) ),
inference(clausify,[status(thm)],[f_38_9]) ).
cnf(f_38_15,plain,
( in(sK58(U_304,U_302,U_300),U_302)
| in(sK55(U_304,U_302,U_300),U_300)
| U_300 = cartesian_product2(U_304,U_302) ),
inference(clausify,[status(thm)],[f_38_9]) ).
cnf(f_38_16,plain,
( sK56(U_304,U_302,U_300) = ordered_pair(sK57(U_304,U_302,U_300),sK58(U_304,U_302,U_300))
| in(sK55(U_304,U_302,U_300),U_300)
| U_300 = cartesian_product2(U_304,U_302) ),
inference(clausify,[status(thm)],[f_38_9]) ).
cnf(f_38_17,plain,
( ~ in(sK56(U_304,U_302,U_300),U_300)
| in(sK55(U_304,U_302,U_300),U_300)
| U_300 = cartesian_product2(U_304,U_302) ),
inference(clausify,[status(thm)],[f_38_9]) ).
cnf(f_38_18,plain,
( in(sK57(U_304,U_302,U_300),U_304)
| sK55(U_304,U_302,U_300) != ordered_pair(U_288,U_287)
| ~ in(U_287,U_302)
| ~ in(U_288,U_304)
| U_300 = cartesian_product2(U_304,U_302) ),
inference(clausify,[status(thm)],[f_38_9]) ).
cnf(f_38_19,plain,
( in(sK58(U_304,U_302,U_300),U_302)
| sK55(U_304,U_302,U_300) != ordered_pair(U_288,U_287)
| ~ in(U_287,U_302)
| ~ in(U_288,U_304)
| U_300 = cartesian_product2(U_304,U_302) ),
inference(clausify,[status(thm)],[f_38_9]) ).
cnf(f_38_20,plain,
( sK56(U_304,U_302,U_300) = ordered_pair(sK57(U_304,U_302,U_300),sK58(U_304,U_302,U_300))
| sK55(U_304,U_302,U_300) != ordered_pair(U_288,U_287)
| ~ in(U_287,U_302)
| ~ in(U_288,U_304)
| U_300 = cartesian_product2(U_304,U_302) ),
inference(clausify,[status(thm)],[f_38_9]) ).
cnf(f_38_21,plain,
( ~ in(sK56(U_304,U_302,U_300),U_300)
| sK55(U_304,U_302,U_300) != ordered_pair(U_288,U_287)
| ~ in(U_287,U_302)
| ~ in(U_288,U_304)
| U_300 = cartesian_product2(U_304,U_302) ),
inference(clausify,[status(thm)],[f_38_9]) ).
fof(f_39_1,plain,
! [A] :
( ( epsilon_connected(A)
| ? [B,C] :
( ~ in(C,B)
& B != C
& ~ in(B,C)
& in(C,A)
& in(B,A) ) )
& ( ! [B,C] :
( in(C,B)
| B = C
| in(B,C)
| ~ in(C,A)
| ~ in(B,A) )
| ~ epsilon_connected(A) ) ),
inference(fof_nnf,[status(thm)],[d3_ordinal1]) ).
fof(f_39_2,plain,
! [U_309] :
( ( epsilon_connected(U_309)
| ? [U_308,U_307] :
( ~ in(U_307,U_308)
& U_308 != U_307
& ~ in(U_308,U_307)
& in(U_307,U_309)
& in(U_308,U_309) ) )
& ( ! [U_306,U_305] :
( in(U_305,U_306)
| U_306 = U_305
| in(U_306,U_305)
| ~ in(U_305,U_309)
| ~ in(U_306,U_309) )
| ~ epsilon_connected(U_309) ) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
( ! [U_311] :
( epsilon_connected(U_311)
| ? [U_308] :
( ? [U_307] :
( ~ in(U_307,U_308)
& U_308 != U_307
& ~ in(U_308,U_307)
& in(U_307,U_311) )
& in(U_308,U_311) ) )
& ! [U_310] :
( ! [U_306] :
( ! [U_305] :
( in(U_305,U_306)
| U_306 = U_305
| in(U_306,U_305)
| ~ in(U_305,U_310) )
| ~ in(U_306,U_310) )
| ~ epsilon_connected(U_310) ) ),
inference(miniscope,[status(thm)],[f_39_2]) ).
fof(f_39_4,plain,
( ! [U_311] :
( epsilon_connected(U_311)
| ( ? [U_307] :
( ~ in(U_307,sK59(U_311))
& sK59(U_311) != U_307
& ~ in(sK59(U_311),U_307)
& in(U_307,U_311) )
& in(sK59(U_311),U_311) ) )
& ! [U_310] :
( ! [U_306] :
( ! [U_305] :
( in(U_305,U_306)
| U_306 = U_305
| in(U_306,U_305)
| ~ in(U_305,U_310) )
| ~ in(U_306,U_310) )
| ~ epsilon_connected(U_310) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_308,sK59(U_311))],[f_39_3]) ).
fof(f_39_5,plain,
( ! [U_311] :
( epsilon_connected(U_311)
| ( ~ in(sK60(U_311),sK59(U_311))
& sK59(U_311) != sK60(U_311)
& ~ in(sK59(U_311),sK60(U_311))
& in(sK60(U_311),U_311)
& in(sK59(U_311),U_311) ) )
& ! [U_310] :
( ! [U_306] :
( ! [U_305] :
( in(U_305,U_306)
| U_306 = U_305
| in(U_306,U_305)
| ~ in(U_305,U_310) )
| ~ in(U_306,U_310) )
| ~ epsilon_connected(U_310) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_307,sK60(U_311))],[f_39_4]) ).
cnf(f_39_6,plain,
( in(U_305,U_306)
| U_306 = U_305
| in(U_306,U_305)
| ~ in(U_305,U_310)
| ~ in(U_306,U_310)
| ~ epsilon_connected(U_310) ),
inference(clausify,[status(thm)],[f_39_5]) ).
cnf(f_39_7,plain,
( in(sK59(U_311),U_311)
| epsilon_connected(U_311) ),
inference(clausify,[status(thm)],[f_39_5]) ).
cnf(f_39_8,plain,
( in(sK60(U_311),U_311)
| epsilon_connected(U_311) ),
inference(clausify,[status(thm)],[f_39_5]) ).
cnf(f_39_9,plain,
( ~ in(sK59(U_311),sK60(U_311))
| epsilon_connected(U_311) ),
inference(clausify,[status(thm)],[f_39_5]) ).
cnf(f_39_10,plain,
( sK59(U_311) != sK60(U_311)
| epsilon_connected(U_311) ),
inference(clausify,[status(thm)],[f_39_5]) ).
cnf(f_39_11,plain,
( ~ in(sK60(U_311),sK59(U_311))
| epsilon_connected(U_311) ),
inference(clausify,[status(thm)],[f_39_5]) ).
fof(f_40_1,plain,
! [A] :
( ! [B] :
( ( ( subset(A,B)
| ? [C,D] :
( ~ in(ordered_pair(C,D),B)
& in(ordered_pair(C,D),A) ) )
& ( ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) )
| ~ subset(A,B) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d3_relat_1]) ).
fof(f_40_2,plain,
! [U_317] :
( ! [U_316] :
( ( ( subset(U_317,U_316)
| ? [U_315,U_314] :
( ~ in(ordered_pair(U_315,U_314),U_316)
& in(ordered_pair(U_315,U_314),U_317) ) )
& ( ! [U_313,U_312] :
( in(ordered_pair(U_313,U_312),U_316)
| ~ in(ordered_pair(U_313,U_312),U_317) )
| ~ subset(U_317,U_316) ) )
| ~ relation(U_316) )
| ~ relation(U_317) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_317] :
( ! [U_316] :
( ( ( subset(U_317,U_316)
| ? [U_314] :
( ~ in(ordered_pair(sK61(U_317,U_316),U_314),U_316)
& in(ordered_pair(sK61(U_317,U_316),U_314),U_317) ) )
& ( ! [U_313,U_312] :
( in(ordered_pair(U_313,U_312),U_316)
| ~ in(ordered_pair(U_313,U_312),U_317) )
| ~ subset(U_317,U_316) ) )
| ~ relation(U_316) )
| ~ relation(U_317) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_315,sK61(U_317,U_316))],[f_40_2]) ).
fof(f_40_4,plain,
! [U_317] :
( ! [U_316] :
( ( ( subset(U_317,U_316)
| ( ~ in(ordered_pair(sK61(U_317,U_316),sK62(U_317,U_316)),U_316)
& in(ordered_pair(sK61(U_317,U_316),sK62(U_317,U_316)),U_317) ) )
& ( ! [U_313,U_312] :
( in(ordered_pair(U_313,U_312),U_316)
| ~ in(ordered_pair(U_313,U_312),U_317) )
| ~ subset(U_317,U_316) ) )
| ~ relation(U_316) )
| ~ relation(U_317) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_314,sK62(U_317,U_316))],[f_40_3]) ).
cnf(f_40_5,plain,
( in(ordered_pair(U_313,U_312),U_316)
| ~ in(ordered_pair(U_313,U_312),U_317)
| ~ subset(U_317,U_316)
| ~ relation(U_316)
| ~ relation(U_317) ),
inference(clausify,[status(thm)],[f_40_4]) ).
cnf(f_40_6,plain,
( in(ordered_pair(sK61(U_317,U_316),sK62(U_317,U_316)),U_317)
| subset(U_317,U_316)
| ~ relation(U_316)
| ~ relation(U_317) ),
inference(clausify,[status(thm)],[f_40_4]) ).
cnf(f_40_7,plain,
( ~ in(ordered_pair(sK61(U_317,U_316),sK62(U_317,U_316)),U_316)
| subset(U_317,U_316)
| ~ relation(U_316)
| ~ relation(U_317) ),
inference(clausify,[status(thm)],[f_40_4]) ).
fof(f_41_1,plain,
! [A,B] :
( ( subset(A,B)
| ? [C] :
( ~ in(C,B)
& in(C,A) ) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(f_41_2,plain,
! [U_321,U_320] :
( ( subset(U_321,U_320)
| ? [U_319] :
( ~ in(U_319,U_320)
& in(U_319,U_321) ) )
& ( ! [U_318] :
( in(U_318,U_320)
| ~ in(U_318,U_321) )
| ~ subset(U_321,U_320) ) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
( ! [U_325,U_323] :
( subset(U_325,U_323)
| ? [U_319] :
( ~ in(U_319,U_323)
& in(U_319,U_325) ) )
& ! [U_324,U_322] :
( ! [U_318] :
( in(U_318,U_322)
| ~ in(U_318,U_324) )
| ~ subset(U_324,U_322) ) ),
inference(miniscope,[status(thm)],[f_41_2]) ).
fof(f_41_4,plain,
( ! [U_325,U_323] :
( subset(U_325,U_323)
| ( ~ in(sK63(U_325,U_323),U_323)
& in(sK63(U_325,U_323),U_325) ) )
& ! [U_324,U_322] :
( ! [U_318] :
( in(U_318,U_322)
| ~ in(U_318,U_324) )
| ~ subset(U_324,U_322) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_319,sK63(U_325,U_323))],[f_41_3]) ).
cnf(f_41_5,plain,
( in(U_318,U_322)
| ~ in(U_318,U_324)
| ~ subset(U_324,U_322) ),
inference(clausify,[status(thm)],[f_41_4]) ).
cnf(f_41_6,plain,
( in(sK63(U_325,U_323),U_325)
| subset(U_325,U_323) ),
inference(clausify,[status(thm)],[f_41_4]) ).
cnf(f_41_7,plain,
( ~ in(sK63(U_325,U_323),U_323)
| subset(U_325,U_323) ),
inference(clausify,[status(thm)],[f_41_4]) ).
fof(f_42_1,plain,
! [A] :
( ! [B] :
( ( is_well_founded_in(A,B)
| ? [C] :
( ! [D] :
( ~ disjoint(fiber(A,D),C)
| ~ in(D,C) )
& C != empty_set
& subset(C,B) ) )
& ( ! [C] :
( ? [D] :
( disjoint(fiber(A,D),C)
& in(D,C) )
| C = empty_set
| ~ subset(C,B) )
| ~ is_well_founded_in(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d3_wellord1]) ).
fof(f_42_2,plain,
! [U_331] :
( ! [U_330] :
( ( is_well_founded_in(U_331,U_330)
| ? [U_329] :
( ! [U_328] :
( ~ disjoint(fiber(U_331,U_328),U_329)
| ~ in(U_328,U_329) )
& U_329 != empty_set
& subset(U_329,U_330) ) )
& ( ! [U_327] :
( ? [U_326] :
( disjoint(fiber(U_331,U_326),U_327)
& in(U_326,U_327) )
| U_327 = empty_set
| ~ subset(U_327,U_330) )
| ~ is_well_founded_in(U_331,U_330) ) )
| ~ relation(U_331) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_331] :
( ( ! [U_333] :
( is_well_founded_in(U_331,U_333)
| ? [U_329] :
( ! [U_328] :
( ~ disjoint(fiber(U_331,U_328),U_329)
| ~ in(U_328,U_329) )
& U_329 != empty_set
& subset(U_329,U_333) ) )
& ! [U_332] :
( ! [U_327] :
( ? [U_326] :
( disjoint(fiber(U_331,U_326),U_327)
& in(U_326,U_327) )
| U_327 = empty_set
| ~ subset(U_327,U_332) )
| ~ is_well_founded_in(U_331,U_332) ) )
| ~ relation(U_331) ),
inference(miniscope,[status(thm)],[f_42_2]) ).
fof(f_42_4,plain,
! [U_331] :
( ( ! [U_333] :
( is_well_founded_in(U_331,U_333)
| ? [U_329] :
( ! [U_328] :
( ~ disjoint(fiber(U_331,U_328),U_329)
| ~ in(U_328,U_329) )
& U_329 != empty_set
& subset(U_329,U_333) ) )
& ! [U_332] :
( ! [U_327] :
( ( disjoint(fiber(U_331,sK64(U_331,U_332,U_327)),U_327)
& in(sK64(U_331,U_332,U_327),U_327) )
| U_327 = empty_set
| ~ subset(U_327,U_332) )
| ~ is_well_founded_in(U_331,U_332) ) )
| ~ relation(U_331) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_326,sK64(U_331,U_332,U_327))],[f_42_3]) ).
fof(f_42_5,plain,
! [U_331] :
( ( ! [U_333] :
( is_well_founded_in(U_331,U_333)
| ( ! [U_328] :
( ~ disjoint(fiber(U_331,U_328),sK65(U_331,U_333))
| ~ in(U_328,sK65(U_331,U_333)) )
& sK65(U_331,U_333) != empty_set
& subset(sK65(U_331,U_333),U_333) ) )
& ! [U_332] :
( ! [U_327] :
( ( disjoint(fiber(U_331,sK64(U_331,U_332,U_327)),U_327)
& in(sK64(U_331,U_332,U_327),U_327) )
| U_327 = empty_set
| ~ subset(U_327,U_332) )
| ~ is_well_founded_in(U_331,U_332) ) )
| ~ relation(U_331) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_329,sK65(U_331,U_333))],[f_42_4]) ).
cnf(f_42_6,plain,
( in(sK64(U_331,U_332,U_327),U_327)
| U_327 = empty_set
| ~ subset(U_327,U_332)
| ~ is_well_founded_in(U_331,U_332)
| ~ relation(U_331) ),
inference(clausify,[status(thm)],[f_42_5]) ).
cnf(f_42_7,plain,
( disjoint(fiber(U_331,sK64(U_331,U_332,U_327)),U_327)
| U_327 = empty_set
| ~ subset(U_327,U_332)
| ~ is_well_founded_in(U_331,U_332)
| ~ relation(U_331) ),
inference(clausify,[status(thm)],[f_42_5]) ).
cnf(f_42_8,plain,
( subset(sK65(U_331,U_333),U_333)
| is_well_founded_in(U_331,U_333)
| ~ relation(U_331) ),
inference(clausify,[status(thm)],[f_42_5]) ).
cnf(f_42_9,plain,
( sK65(U_331,U_333) != empty_set
| is_well_founded_in(U_331,U_333)
| ~ relation(U_331) ),
inference(clausify,[status(thm)],[f_42_5]) ).
cnf(f_42_10,plain,
( ~ disjoint(fiber(U_331,U_328),sK65(U_331,U_333))
| ~ in(U_328,sK65(U_331,U_333))
| is_well_founded_in(U_331,U_333)
| ~ relation(U_331) ),
inference(clausify,[status(thm)],[f_42_5]) ).
fof(f_43_1,plain,
! [A,B,C] :
( ( C = set_intersection2(A,B)
| ? [D] :
( ( ~ in(D,C)
& in(D,B)
& in(D,A) )
| ( ( ~ in(D,B)
| ~ in(D,A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ~ in(D,B)
| ~ in(D,A) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_xboole_0]) ).
fof(f_43_2,plain,
! [U_338,U_337,U_336] :
( ( U_336 = set_intersection2(U_338,U_337)
| ? [U_335] :
( ( ~ in(U_335,U_336)
& in(U_335,U_337)
& in(U_335,U_338) )
| ( ( ~ in(U_335,U_337)
| ~ in(U_335,U_338) )
& in(U_335,U_336) ) ) )
& ( ! [U_334] :
( ( in(U_334,U_336)
| ~ in(U_334,U_337)
| ~ in(U_334,U_338) )
& ( ( in(U_334,U_337)
& in(U_334,U_338) )
| ~ in(U_334,U_336) ) )
| U_336 != set_intersection2(U_338,U_337) ) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
( ! [U_348,U_346,U_344] :
( U_344 = set_intersection2(U_348,U_346)
| ? [U_342] :
( ~ in(U_342,U_344)
& in(U_342,U_346)
& in(U_342,U_348) )
| ? [U_341] :
( ( ~ in(U_341,U_346)
| ~ in(U_341,U_348) )
& in(U_341,U_344) ) )
& ! [U_347,U_345,U_343] :
( ( ! [U_340] :
( in(U_340,U_343)
| ~ in(U_340,U_345)
| ~ in(U_340,U_347) )
& ! [U_339] :
( ( in(U_339,U_345)
& in(U_339,U_347) )
| ~ in(U_339,U_343) ) )
| U_343 != set_intersection2(U_347,U_345) ) ),
inference(miniscope,[status(thm)],[f_43_2]) ).
fof(f_43_4,plain,
( ! [U_348,U_346,U_344] :
( U_344 = set_intersection2(U_348,U_346)
| ? [U_342] :
( ~ in(U_342,U_344)
& in(U_342,U_346)
& in(U_342,U_348) )
| ( ( ~ in(sK66(U_348,U_346,U_344),U_346)
| ~ in(sK66(U_348,U_346,U_344),U_348) )
& in(sK66(U_348,U_346,U_344),U_344) ) )
& ! [U_347,U_345,U_343] :
( ( ! [U_340] :
( in(U_340,U_343)
| ~ in(U_340,U_345)
| ~ in(U_340,U_347) )
& ! [U_339] :
( ( in(U_339,U_345)
& in(U_339,U_347) )
| ~ in(U_339,U_343) ) )
| U_343 != set_intersection2(U_347,U_345) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_341,sK66(U_348,U_346,U_344))],[f_43_3]) ).
fof(f_43_5,plain,
( ! [U_348,U_346,U_344] :
( U_344 = set_intersection2(U_348,U_346)
| ( ~ in(sK67(U_348,U_346,U_344),U_344)
& in(sK67(U_348,U_346,U_344),U_346)
& in(sK67(U_348,U_346,U_344),U_348) )
| ( ( ~ in(sK66(U_348,U_346,U_344),U_346)
| ~ in(sK66(U_348,U_346,U_344),U_348) )
& in(sK66(U_348,U_346,U_344),U_344) ) )
& ! [U_347,U_345,U_343] :
( ( ! [U_340] :
( in(U_340,U_343)
| ~ in(U_340,U_345)
| ~ in(U_340,U_347) )
& ! [U_339] :
( ( in(U_339,U_345)
& in(U_339,U_347) )
| ~ in(U_339,U_343) ) )
| U_343 != set_intersection2(U_347,U_345) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_342,sK67(U_348,U_346,U_344))],[f_43_4]) ).
cnf(f_43_6,plain,
( in(U_339,U_347)
| ~ in(U_339,U_343)
| U_343 != set_intersection2(U_347,U_345) ),
inference(clausify,[status(thm)],[f_43_5]) ).
cnf(f_43_7,plain,
( in(U_339,U_345)
| ~ in(U_339,U_343)
| U_343 != set_intersection2(U_347,U_345) ),
inference(clausify,[status(thm)],[f_43_5]) ).
cnf(f_43_8,plain,
( in(U_340,U_343)
| ~ in(U_340,U_345)
| ~ in(U_340,U_347)
| U_343 != set_intersection2(U_347,U_345) ),
inference(clausify,[status(thm)],[f_43_5]) ).
cnf(f_43_9,plain,
( in(sK67(U_348,U_346,U_344),U_348)
| in(sK66(U_348,U_346,U_344),U_344)
| U_344 = set_intersection2(U_348,U_346) ),
inference(clausify,[status(thm)],[f_43_5]) ).
cnf(f_43_10,plain,
( in(sK67(U_348,U_346,U_344),U_346)
| in(sK66(U_348,U_346,U_344),U_344)
| U_344 = set_intersection2(U_348,U_346) ),
inference(clausify,[status(thm)],[f_43_5]) ).
cnf(f_43_11,plain,
( ~ in(sK67(U_348,U_346,U_344),U_344)
| in(sK66(U_348,U_346,U_344),U_344)
| U_344 = set_intersection2(U_348,U_346) ),
inference(clausify,[status(thm)],[f_43_5]) ).
cnf(f_43_12,plain,
( in(sK67(U_348,U_346,U_344),U_348)
| ~ in(sK66(U_348,U_346,U_344),U_346)
| ~ in(sK66(U_348,U_346,U_344),U_348)
| U_344 = set_intersection2(U_348,U_346) ),
inference(clausify,[status(thm)],[f_43_5]) ).
cnf(f_43_13,plain,
( in(sK67(U_348,U_346,U_344),U_346)
| ~ in(sK66(U_348,U_346,U_344),U_346)
| ~ in(sK66(U_348,U_346,U_344),U_348)
| U_344 = set_intersection2(U_348,U_346) ),
inference(clausify,[status(thm)],[f_43_5]) ).
cnf(f_43_14,plain,
( ~ in(sK67(U_348,U_346,U_344),U_344)
| ~ in(sK66(U_348,U_346,U_344),U_346)
| ~ in(sK66(U_348,U_346,U_344),U_348)
| U_344 = set_intersection2(U_348,U_346) ),
inference(clausify,[status(thm)],[f_43_5]) ).
fof(f_44_1,plain,
! [A] :
( ! [B,C] :
( ( ( ( C = apply(A,B)
| C != empty_set )
& ( C = empty_set
| C != apply(A,B) ) )
| in(B,relation_dom(A)) )
& ( ( ( C = apply(A,B)
| ~ in(ordered_pair(B,C),A) )
& ( in(ordered_pair(B,C),A)
| C != apply(A,B) ) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d4_funct_1]) ).
fof(f_44_2,plain,
! [U_351] :
( ! [U_350,U_349] :
( ( ( ( U_349 = apply(U_351,U_350)
| U_349 != empty_set )
& ( U_349 = empty_set
| U_349 != apply(U_351,U_350) ) )
| in(U_350,relation_dom(U_351)) )
& ( ( ( U_349 = apply(U_351,U_350)
| ~ in(ordered_pair(U_350,U_349),U_351) )
& ( in(ordered_pair(U_350,U_349),U_351)
| U_349 != apply(U_351,U_350) ) )
| ~ in(U_350,relation_dom(U_351)) ) )
| ~ function(U_351)
| ~ relation(U_351) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_351] :
( ( ! [U_359] :
( ( ! [U_357] :
( U_357 = apply(U_351,U_359)
| U_357 != empty_set )
& ! [U_356] :
( U_356 = empty_set
| U_356 != apply(U_351,U_359) ) )
| in(U_359,relation_dom(U_351)) )
& ! [U_358] :
( ( ! [U_355] :
( U_355 = apply(U_351,U_358)
| ~ in(ordered_pair(U_358,U_355),U_351) )
& ! [U_354] :
( in(ordered_pair(U_358,U_354),U_351)
| U_354 != apply(U_351,U_358) ) )
| ~ in(U_358,relation_dom(U_351)) ) )
| ~ function(U_351)
| ~ relation(U_351) ),
inference(miniscope,[status(thm)],[f_44_2]) ).
cnf(f_44_4,plain,
( in(ordered_pair(U_358,U_354),U_351)
| U_354 != apply(U_351,U_358)
| ~ in(U_358,relation_dom(U_351))
| ~ function(U_351)
| ~ relation(U_351) ),
inference(clausify,[status(thm)],[f_44_3]) ).
cnf(f_44_5,plain,
( U_355 = apply(U_351,U_358)
| ~ in(ordered_pair(U_358,U_355),U_351)
| ~ in(U_358,relation_dom(U_351))
| ~ function(U_351)
| ~ relation(U_351) ),
inference(clausify,[status(thm)],[f_44_3]) ).
cnf(f_44_6,plain,
( U_356 = empty_set
| U_356 != apply(U_351,U_359)
| in(U_359,relation_dom(U_351))
| ~ function(U_351)
| ~ relation(U_351) ),
inference(clausify,[status(thm)],[f_44_3]) ).
cnf(f_44_7,plain,
( U_357 = apply(U_351,U_359)
| U_357 != empty_set
| in(U_359,relation_dom(U_351))
| ~ function(U_351)
| ~ relation(U_351) ),
inference(clausify,[status(thm)],[f_44_3]) ).
fof(f_45_1,plain,
! [A] :
( ( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) )
& ( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ) ),
inference(fof_nnf,[status(thm)],[d4_ordinal1]) ).
fof(f_45_2,plain,
! [U_360] :
( ( ordinal(U_360)
| ~ epsilon_connected(U_360)
| ~ epsilon_transitive(U_360) )
& ( ( epsilon_connected(U_360)
& epsilon_transitive(U_360) )
| ~ ordinal(U_360) ) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
( ! [U_362] :
( ordinal(U_362)
| ~ epsilon_connected(U_362)
| ~ epsilon_transitive(U_362) )
& ! [U_361] :
( ( epsilon_connected(U_361)
& epsilon_transitive(U_361) )
| ~ ordinal(U_361) ) ),
inference(miniscope,[status(thm)],[f_45_2]) ).
cnf(f_45_4,plain,
( epsilon_transitive(U_361)
| ~ ordinal(U_361) ),
inference(clausify,[status(thm)],[f_45_3]) ).
cnf(f_45_5,plain,
( epsilon_connected(U_361)
| ~ ordinal(U_361) ),
inference(clausify,[status(thm)],[f_45_3]) ).
cnf(f_45_6,plain,
( ordinal(U_362)
| ~ epsilon_connected(U_362)
| ~ epsilon_transitive(U_362) ),
inference(clausify,[status(thm)],[f_45_3]) ).
fof(f_46_1,plain,
! [A] :
( ! [B] :
( ( B = relation_dom(A)
| ? [C] :
( ( ~ in(C,B)
& ? [D] : in(ordered_pair(C,D),A) )
| ( ! [D] : ~ in(ordered_pair(C,D),A)
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) )
& ( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d4_relat_1]) ).
fof(f_46_2,plain,
! [U_370] :
( ! [U_369] :
( ( U_369 = relation_dom(U_370)
| ? [U_368] :
( ( ~ in(U_368,U_369)
& ? [U_367] : in(ordered_pair(U_368,U_367),U_370) )
| ( ! [U_366] : ~ in(ordered_pair(U_368,U_366),U_370)
& in(U_368,U_369) ) ) )
& ( ! [U_365] :
( ( in(U_365,U_369)
| ! [U_364] : ~ in(ordered_pair(U_365,U_364),U_370) )
& ( ? [U_363] : in(ordered_pair(U_365,U_363),U_370)
| ~ in(U_365,U_369) ) )
| U_369 != relation_dom(U_370) ) )
| ~ relation(U_370) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_370] :
( ( ! [U_376] :
( U_376 = relation_dom(U_370)
| ? [U_374] :
( ~ in(U_374,U_376)
& ? [U_367] : in(ordered_pair(U_374,U_367),U_370) )
| ? [U_373] :
( ! [U_366] : ~ in(ordered_pair(U_373,U_366),U_370)
& in(U_373,U_376) ) )
& ! [U_375] :
( ( ! [U_372] :
( in(U_372,U_375)
| ! [U_364] : ~ in(ordered_pair(U_372,U_364),U_370) )
& ! [U_371] :
( ? [U_363] : in(ordered_pair(U_371,U_363),U_370)
| ~ in(U_371,U_375) ) )
| U_375 != relation_dom(U_370) ) )
| ~ relation(U_370) ),
inference(miniscope,[status(thm)],[f_46_2]) ).
fof(f_46_4,plain,
! [U_370] :
( ( ! [U_376] :
( U_376 = relation_dom(U_370)
| ? [U_374] :
( ~ in(U_374,U_376)
& ? [U_367] : in(ordered_pair(U_374,U_367),U_370) )
| ? [U_373] :
( ! [U_366] : ~ in(ordered_pair(U_373,U_366),U_370)
& in(U_373,U_376) ) )
& ! [U_375] :
( ( ! [U_372] :
( in(U_372,U_375)
| ! [U_364] : ~ in(ordered_pair(U_372,U_364),U_370) )
& ! [U_371] :
( in(ordered_pair(U_371,sK68(U_370,U_375,U_371)),U_370)
| ~ in(U_371,U_375) ) )
| U_375 != relation_dom(U_370) ) )
| ~ relation(U_370) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_363,sK68(U_370,U_375,U_371))],[f_46_3]) ).
fof(f_46_5,plain,
! [U_370] :
( ( ! [U_376] :
( U_376 = relation_dom(U_370)
| ? [U_374] :
( ~ in(U_374,U_376)
& ? [U_367] : in(ordered_pair(U_374,U_367),U_370) )
| ( ! [U_366] : ~ in(ordered_pair(sK69(U_370,U_376),U_366),U_370)
& in(sK69(U_370,U_376),U_376) ) )
& ! [U_375] :
( ( ! [U_372] :
( in(U_372,U_375)
| ! [U_364] : ~ in(ordered_pair(U_372,U_364),U_370) )
& ! [U_371] :
( in(ordered_pair(U_371,sK68(U_370,U_375,U_371)),U_370)
| ~ in(U_371,U_375) ) )
| U_375 != relation_dom(U_370) ) )
| ~ relation(U_370) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_373,sK69(U_370,U_376))],[f_46_4]) ).
fof(f_46_6,plain,
! [U_370] :
( ( ! [U_376] :
( U_376 = relation_dom(U_370)
| ( ~ in(sK70(U_370,U_376),U_376)
& ? [U_367] : in(ordered_pair(sK70(U_370,U_376),U_367),U_370) )
| ( ! [U_366] : ~ in(ordered_pair(sK69(U_370,U_376),U_366),U_370)
& in(sK69(U_370,U_376),U_376) ) )
& ! [U_375] :
( ( ! [U_372] :
( in(U_372,U_375)
| ! [U_364] : ~ in(ordered_pair(U_372,U_364),U_370) )
& ! [U_371] :
( in(ordered_pair(U_371,sK68(U_370,U_375,U_371)),U_370)
| ~ in(U_371,U_375) ) )
| U_375 != relation_dom(U_370) ) )
| ~ relation(U_370) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_374,sK70(U_370,U_376))],[f_46_5]) ).
fof(f_46_7,plain,
! [U_370] :
( ( ! [U_376] :
( U_376 = relation_dom(U_370)
| ( ~ in(sK70(U_370,U_376),U_376)
& in(ordered_pair(sK70(U_370,U_376),sK71(U_370,U_376)),U_370) )
| ( ! [U_366] : ~ in(ordered_pair(sK69(U_370,U_376),U_366),U_370)
& in(sK69(U_370,U_376),U_376) ) )
& ! [U_375] :
( ( ! [U_372] :
( in(U_372,U_375)
| ! [U_364] : ~ in(ordered_pair(U_372,U_364),U_370) )
& ! [U_371] :
( in(ordered_pair(U_371,sK68(U_370,U_375,U_371)),U_370)
| ~ in(U_371,U_375) ) )
| U_375 != relation_dom(U_370) ) )
| ~ relation(U_370) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_367,sK71(U_370,U_376))],[f_46_6]) ).
cnf(f_46_8,plain,
( in(ordered_pair(U_371,sK68(U_370,U_375,U_371)),U_370)
| ~ in(U_371,U_375)
| U_375 != relation_dom(U_370)
| ~ relation(U_370) ),
inference(clausify,[status(thm)],[f_46_7]) ).
cnf(f_46_9,plain,
( in(U_372,U_375)
| ~ in(ordered_pair(U_372,U_364),U_370)
| U_375 != relation_dom(U_370)
| ~ relation(U_370) ),
inference(clausify,[status(thm)],[f_46_7]) ).
cnf(f_46_10,plain,
( in(ordered_pair(sK70(U_370,U_376),sK71(U_370,U_376)),U_370)
| in(sK69(U_370,U_376),U_376)
| U_376 = relation_dom(U_370)
| ~ relation(U_370) ),
inference(clausify,[status(thm)],[f_46_7]) ).
cnf(f_46_11,plain,
( ~ in(sK70(U_370,U_376),U_376)
| in(sK69(U_370,U_376),U_376)
| U_376 = relation_dom(U_370)
| ~ relation(U_370) ),
inference(clausify,[status(thm)],[f_46_7]) ).
cnf(f_46_12,plain,
( in(ordered_pair(sK70(U_370,U_376),sK71(U_370,U_376)),U_370)
| ~ in(ordered_pair(sK69(U_370,U_376),U_366),U_370)
| U_376 = relation_dom(U_370)
| ~ relation(U_370) ),
inference(clausify,[status(thm)],[f_46_7]) ).
cnf(f_46_13,plain,
( ~ in(sK70(U_370,U_376),U_376)
| ~ in(ordered_pair(sK69(U_370,U_376),U_366),U_370)
| U_376 = relation_dom(U_370)
| ~ relation(U_370) ),
inference(clausify,[status(thm)],[f_46_7]) ).
fof(f_47_1,plain,
! [A] :
( ! [B] :
( ( is_antisymmetric_in(A,B)
| ? [C,D] :
( C != D
& in(ordered_pair(D,C),A)
& in(ordered_pair(C,D),A)
& in(D,B)
& in(C,B) ) )
& ( ! [C,D] :
( C = D
| ~ in(ordered_pair(D,C),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(D,B)
| ~ in(C,B) )
| ~ is_antisymmetric_in(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d4_relat_2]) ).
fof(f_47_2,plain,
! [U_382] :
( ! [U_381] :
( ( is_antisymmetric_in(U_382,U_381)
| ? [U_380,U_379] :
( U_380 != U_379
& in(ordered_pair(U_379,U_380),U_382)
& in(ordered_pair(U_380,U_379),U_382)
& in(U_379,U_381)
& in(U_380,U_381) ) )
& ( ! [U_378,U_377] :
( U_378 = U_377
| ~ in(ordered_pair(U_377,U_378),U_382)
| ~ in(ordered_pair(U_378,U_377),U_382)
| ~ in(U_377,U_381)
| ~ in(U_378,U_381) )
| ~ is_antisymmetric_in(U_382,U_381) ) )
| ~ relation(U_382) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_382] :
( ( ! [U_384] :
( is_antisymmetric_in(U_382,U_384)
| ? [U_380,U_379] :
( U_380 != U_379
& in(ordered_pair(U_379,U_380),U_382)
& in(ordered_pair(U_380,U_379),U_382)
& in(U_379,U_384)
& in(U_380,U_384) ) )
& ! [U_383] :
( ! [U_378,U_377] :
( U_378 = U_377
| ~ in(ordered_pair(U_377,U_378),U_382)
| ~ in(ordered_pair(U_378,U_377),U_382)
| ~ in(U_377,U_383)
| ~ in(U_378,U_383) )
| ~ is_antisymmetric_in(U_382,U_383) ) )
| ~ relation(U_382) ),
inference(miniscope,[status(thm)],[f_47_2]) ).
fof(f_47_4,plain,
! [U_382] :
( ( ! [U_384] :
( is_antisymmetric_in(U_382,U_384)
| ? [U_379] :
( sK72(U_382,U_384) != U_379
& in(ordered_pair(U_379,sK72(U_382,U_384)),U_382)
& in(ordered_pair(sK72(U_382,U_384),U_379),U_382)
& in(U_379,U_384)
& in(sK72(U_382,U_384),U_384) ) )
& ! [U_383] :
( ! [U_378,U_377] :
( U_378 = U_377
| ~ in(ordered_pair(U_377,U_378),U_382)
| ~ in(ordered_pair(U_378,U_377),U_382)
| ~ in(U_377,U_383)
| ~ in(U_378,U_383) )
| ~ is_antisymmetric_in(U_382,U_383) ) )
| ~ relation(U_382) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_380,sK72(U_382,U_384))],[f_47_3]) ).
fof(f_47_5,plain,
! [U_382] :
( ( ! [U_384] :
( is_antisymmetric_in(U_382,U_384)
| ( sK72(U_382,U_384) != sK73(U_382,U_384)
& in(ordered_pair(sK73(U_382,U_384),sK72(U_382,U_384)),U_382)
& in(ordered_pair(sK72(U_382,U_384),sK73(U_382,U_384)),U_382)
& in(sK73(U_382,U_384),U_384)
& in(sK72(U_382,U_384),U_384) ) )
& ! [U_383] :
( ! [U_378,U_377] :
( U_378 = U_377
| ~ in(ordered_pair(U_377,U_378),U_382)
| ~ in(ordered_pair(U_378,U_377),U_382)
| ~ in(U_377,U_383)
| ~ in(U_378,U_383) )
| ~ is_antisymmetric_in(U_382,U_383) ) )
| ~ relation(U_382) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_379,sK73(U_382,U_384))],[f_47_4]) ).
cnf(f_47_6,plain,
( U_378 = U_377
| ~ in(ordered_pair(U_377,U_378),U_382)
| ~ in(ordered_pair(U_378,U_377),U_382)
| ~ in(U_377,U_383)
| ~ in(U_378,U_383)
| ~ is_antisymmetric_in(U_382,U_383)
| ~ relation(U_382) ),
inference(clausify,[status(thm)],[f_47_5]) ).
cnf(f_47_7,plain,
( in(sK72(U_382,U_384),U_384)
| is_antisymmetric_in(U_382,U_384)
| ~ relation(U_382) ),
inference(clausify,[status(thm)],[f_47_5]) ).
cnf(f_47_8,plain,
( in(sK73(U_382,U_384),U_384)
| is_antisymmetric_in(U_382,U_384)
| ~ relation(U_382) ),
inference(clausify,[status(thm)],[f_47_5]) ).
cnf(f_47_9,plain,
( in(ordered_pair(sK72(U_382,U_384),sK73(U_382,U_384)),U_382)
| is_antisymmetric_in(U_382,U_384)
| ~ relation(U_382) ),
inference(clausify,[status(thm)],[f_47_5]) ).
cnf(f_47_10,plain,
( in(ordered_pair(sK73(U_382,U_384),sK72(U_382,U_384)),U_382)
| is_antisymmetric_in(U_382,U_384)
| ~ relation(U_382) ),
inference(clausify,[status(thm)],[f_47_5]) ).
cnf(f_47_11,plain,
( sK72(U_382,U_384) != sK73(U_382,U_384)
| is_antisymmetric_in(U_382,U_384)
| ~ relation(U_382) ),
inference(clausify,[status(thm)],[f_47_5]) ).
fof(f_48_1,plain,
! [A] : cast_to_subset(A) = A,
inference(fof_nnf,[status(thm)],[d4_subset_1]) ).
fof(f_48_2,plain,
! [U_385] : cast_to_subset(U_385) = U_385,
inference(variable_rename,[status(thm)],[f_48_1]) ).
cnf(f_48_3,plain,
cast_to_subset(U_385) = U_385,
inference(clausify,[status(thm)],[f_48_2]) ).
fof(f_49_1,plain,
! [A,B] :
( ( B = union(A)
| ? [C] :
( ( ~ in(C,B)
& ? [D] :
( in(D,A)
& in(C,D) ) )
| ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ! [D] :
( ~ in(D,A)
| ~ in(C,D) ) )
& ( ? [D] :
( in(D,A)
& in(C,D) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(fof_nnf,[status(thm)],[d4_tarski]) ).
fof(f_49_2,plain,
! [U_393,U_392] :
( ( U_392 = union(U_393)
| ? [U_391] :
( ( ~ in(U_391,U_392)
& ? [U_390] :
( in(U_390,U_393)
& in(U_391,U_390) ) )
| ( ! [U_389] :
( ~ in(U_389,U_393)
| ~ in(U_391,U_389) )
& in(U_391,U_392) ) ) )
& ( ! [U_388] :
( ( in(U_388,U_392)
| ! [U_387] :
( ~ in(U_387,U_393)
| ~ in(U_388,U_387) ) )
& ( ? [U_386] :
( in(U_386,U_393)
& in(U_388,U_386) )
| ~ in(U_388,U_392) ) )
| U_392 != union(U_393) ) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
( ! [U_401,U_399] :
( U_399 = union(U_401)
| ? [U_397] :
( ~ in(U_397,U_399)
& ? [U_390] :
( in(U_390,U_401)
& in(U_397,U_390) ) )
| ? [U_396] :
( ! [U_389] :
( ~ in(U_389,U_401)
| ~ in(U_396,U_389) )
& in(U_396,U_399) ) )
& ! [U_400,U_398] :
( ( ! [U_395] :
( in(U_395,U_398)
| ! [U_387] :
( ~ in(U_387,U_400)
| ~ in(U_395,U_387) ) )
& ! [U_394] :
( ? [U_386] :
( in(U_386,U_400)
& in(U_394,U_386) )
| ~ in(U_394,U_398) ) )
| U_398 != union(U_400) ) ),
inference(miniscope,[status(thm)],[f_49_2]) ).
fof(f_49_4,plain,
( ! [U_401,U_399] :
( U_399 = union(U_401)
| ? [U_397] :
( ~ in(U_397,U_399)
& ? [U_390] :
( in(U_390,U_401)
& in(U_397,U_390) ) )
| ? [U_396] :
( ! [U_389] :
( ~ in(U_389,U_401)
| ~ in(U_396,U_389) )
& in(U_396,U_399) ) )
& ! [U_400,U_398] :
( ( ! [U_395] :
( in(U_395,U_398)
| ! [U_387] :
( ~ in(U_387,U_400)
| ~ in(U_395,U_387) ) )
& ! [U_394] :
( ( in(sK74(U_400,U_398,U_394),U_400)
& in(U_394,sK74(U_400,U_398,U_394)) )
| ~ in(U_394,U_398) ) )
| U_398 != union(U_400) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_386,sK74(U_400,U_398,U_394))],[f_49_3]) ).
fof(f_49_5,plain,
( ! [U_401,U_399] :
( U_399 = union(U_401)
| ? [U_397] :
( ~ in(U_397,U_399)
& ? [U_390] :
( in(U_390,U_401)
& in(U_397,U_390) ) )
| ( ! [U_389] :
( ~ in(U_389,U_401)
| ~ in(sK75(U_401,U_399),U_389) )
& in(sK75(U_401,U_399),U_399) ) )
& ! [U_400,U_398] :
( ( ! [U_395] :
( in(U_395,U_398)
| ! [U_387] :
( ~ in(U_387,U_400)
| ~ in(U_395,U_387) ) )
& ! [U_394] :
( ( in(sK74(U_400,U_398,U_394),U_400)
& in(U_394,sK74(U_400,U_398,U_394)) )
| ~ in(U_394,U_398) ) )
| U_398 != union(U_400) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_396,sK75(U_401,U_399))],[f_49_4]) ).
fof(f_49_6,plain,
( ! [U_401,U_399] :
( U_399 = union(U_401)
| ( ~ in(sK76(U_401,U_399),U_399)
& ? [U_390] :
( in(U_390,U_401)
& in(sK76(U_401,U_399),U_390) ) )
| ( ! [U_389] :
( ~ in(U_389,U_401)
| ~ in(sK75(U_401,U_399),U_389) )
& in(sK75(U_401,U_399),U_399) ) )
& ! [U_400,U_398] :
( ( ! [U_395] :
( in(U_395,U_398)
| ! [U_387] :
( ~ in(U_387,U_400)
| ~ in(U_395,U_387) ) )
& ! [U_394] :
( ( in(sK74(U_400,U_398,U_394),U_400)
& in(U_394,sK74(U_400,U_398,U_394)) )
| ~ in(U_394,U_398) ) )
| U_398 != union(U_400) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_397,sK76(U_401,U_399))],[f_49_5]) ).
fof(f_49_7,plain,
( ! [U_401,U_399] :
( U_399 = union(U_401)
| ( ~ in(sK76(U_401,U_399),U_399)
& in(sK77(U_401,U_399),U_401)
& in(sK76(U_401,U_399),sK77(U_401,U_399)) )
| ( ! [U_389] :
( ~ in(U_389,U_401)
| ~ in(sK75(U_401,U_399),U_389) )
& in(sK75(U_401,U_399),U_399) ) )
& ! [U_400,U_398] :
( ( ! [U_395] :
( in(U_395,U_398)
| ! [U_387] :
( ~ in(U_387,U_400)
| ~ in(U_395,U_387) ) )
& ! [U_394] :
( ( in(sK74(U_400,U_398,U_394),U_400)
& in(U_394,sK74(U_400,U_398,U_394)) )
| ~ in(U_394,U_398) ) )
| U_398 != union(U_400) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_390,sK77(U_401,U_399))],[f_49_6]) ).
cnf(f_49_8,plain,
( in(U_394,sK74(U_400,U_398,U_394))
| ~ in(U_394,U_398)
| U_398 != union(U_400) ),
inference(clausify,[status(thm)],[f_49_7]) ).
cnf(f_49_9,plain,
( in(sK74(U_400,U_398,U_394),U_400)
| ~ in(U_394,U_398)
| U_398 != union(U_400) ),
inference(clausify,[status(thm)],[f_49_7]) ).
cnf(f_49_10,plain,
( in(U_395,U_398)
| ~ in(U_387,U_400)
| ~ in(U_395,U_387)
| U_398 != union(U_400) ),
inference(clausify,[status(thm)],[f_49_7]) ).
cnf(f_49_11,plain,
( in(sK76(U_401,U_399),sK77(U_401,U_399))
| in(sK75(U_401,U_399),U_399)
| U_399 = union(U_401) ),
inference(clausify,[status(thm)],[f_49_7]) ).
cnf(f_49_12,plain,
( in(sK77(U_401,U_399),U_401)
| in(sK75(U_401,U_399),U_399)
| U_399 = union(U_401) ),
inference(clausify,[status(thm)],[f_49_7]) ).
cnf(f_49_13,plain,
( ~ in(sK76(U_401,U_399),U_399)
| in(sK75(U_401,U_399),U_399)
| U_399 = union(U_401) ),
inference(clausify,[status(thm)],[f_49_7]) ).
cnf(f_49_14,plain,
( in(sK76(U_401,U_399),sK77(U_401,U_399))
| ~ in(U_389,U_401)
| ~ in(sK75(U_401,U_399),U_389)
| U_399 = union(U_401) ),
inference(clausify,[status(thm)],[f_49_7]) ).
cnf(f_49_15,plain,
( in(sK77(U_401,U_399),U_401)
| ~ in(U_389,U_401)
| ~ in(sK75(U_401,U_399),U_389)
| U_399 = union(U_401) ),
inference(clausify,[status(thm)],[f_49_7]) ).
cnf(f_49_16,plain,
( ~ in(sK76(U_401,U_399),U_399)
| ~ in(U_389,U_401)
| ~ in(sK75(U_401,U_399),U_389)
| U_399 = union(U_401) ),
inference(clausify,[status(thm)],[f_49_7]) ).
fof(f_50_1,plain,
! [A] :
( ( ( well_ordering(A)
| ~ well_founded_relation(A)
| ~ connected(A)
| ~ antisymmetric(A)
| ~ transitive(A)
| ~ reflexive(A) )
& ( ( well_founded_relation(A)
& connected(A)
& antisymmetric(A)
& transitive(A)
& reflexive(A) )
| ~ well_ordering(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d4_wellord1]) ).
fof(f_50_2,plain,
! [U_402] :
( ( ( well_ordering(U_402)
| ~ well_founded_relation(U_402)
| ~ connected(U_402)
| ~ antisymmetric(U_402)
| ~ transitive(U_402)
| ~ reflexive(U_402) )
& ( ( well_founded_relation(U_402)
& connected(U_402)
& antisymmetric(U_402)
& transitive(U_402)
& reflexive(U_402) )
| ~ well_ordering(U_402) ) )
| ~ relation(U_402) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
cnf(f_50_3,plain,
( reflexive(U_402)
| ~ well_ordering(U_402)
| ~ relation(U_402) ),
inference(clausify,[status(thm)],[f_50_2]) ).
cnf(f_50_4,plain,
( transitive(U_402)
| ~ well_ordering(U_402)
| ~ relation(U_402) ),
inference(clausify,[status(thm)],[f_50_2]) ).
cnf(f_50_5,plain,
( antisymmetric(U_402)
| ~ well_ordering(U_402)
| ~ relation(U_402) ),
inference(clausify,[status(thm)],[f_50_2]) ).
cnf(f_50_6,plain,
( connected(U_402)
| ~ well_ordering(U_402)
| ~ relation(U_402) ),
inference(clausify,[status(thm)],[f_50_2]) ).
cnf(f_50_7,plain,
( well_founded_relation(U_402)
| ~ well_ordering(U_402)
| ~ relation(U_402) ),
inference(clausify,[status(thm)],[f_50_2]) ).
cnf(f_50_8,plain,
( well_ordering(U_402)
| ~ well_founded_relation(U_402)
| ~ connected(U_402)
| ~ antisymmetric(U_402)
| ~ transitive(U_402)
| ~ reflexive(U_402)
| ~ relation(U_402) ),
inference(clausify,[status(thm)],[f_50_2]) ).
fof(f_51_1,plain,
! [A,B,C] :
( ( C = set_difference(A,B)
| ? [D] :
( ( ~ in(D,C)
& ~ in(D,B)
& in(D,A) )
| ( ( in(D,B)
| ~ in(D,A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| in(D,B)
| ~ in(D,A) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(fof_nnf,[status(thm)],[d4_xboole_0]) ).
fof(f_51_2,plain,
! [U_407,U_406,U_405] :
( ( U_405 = set_difference(U_407,U_406)
| ? [U_404] :
( ( ~ in(U_404,U_405)
& ~ in(U_404,U_406)
& in(U_404,U_407) )
| ( ( in(U_404,U_406)
| ~ in(U_404,U_407) )
& in(U_404,U_405) ) ) )
& ( ! [U_403] :
( ( in(U_403,U_405)
| in(U_403,U_406)
| ~ in(U_403,U_407) )
& ( ( ~ in(U_403,U_406)
& in(U_403,U_407) )
| ~ in(U_403,U_405) ) )
| U_405 != set_difference(U_407,U_406) ) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
( ! [U_417,U_415,U_413] :
( U_413 = set_difference(U_417,U_415)
| ? [U_411] :
( ~ in(U_411,U_413)
& ~ in(U_411,U_415)
& in(U_411,U_417) )
| ? [U_410] :
( ( in(U_410,U_415)
| ~ in(U_410,U_417) )
& in(U_410,U_413) ) )
& ! [U_416,U_414,U_412] :
( ( ! [U_409] :
( in(U_409,U_412)
| in(U_409,U_414)
| ~ in(U_409,U_416) )
& ! [U_408] :
( ( ~ in(U_408,U_414)
& in(U_408,U_416) )
| ~ in(U_408,U_412) ) )
| U_412 != set_difference(U_416,U_414) ) ),
inference(miniscope,[status(thm)],[f_51_2]) ).
fof(f_51_4,plain,
( ! [U_417,U_415,U_413] :
( U_413 = set_difference(U_417,U_415)
| ? [U_411] :
( ~ in(U_411,U_413)
& ~ in(U_411,U_415)
& in(U_411,U_417) )
| ( ( in(sK78(U_417,U_415,U_413),U_415)
| ~ in(sK78(U_417,U_415,U_413),U_417) )
& in(sK78(U_417,U_415,U_413),U_413) ) )
& ! [U_416,U_414,U_412] :
( ( ! [U_409] :
( in(U_409,U_412)
| in(U_409,U_414)
| ~ in(U_409,U_416) )
& ! [U_408] :
( ( ~ in(U_408,U_414)
& in(U_408,U_416) )
| ~ in(U_408,U_412) ) )
| U_412 != set_difference(U_416,U_414) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_410,sK78(U_417,U_415,U_413))],[f_51_3]) ).
fof(f_51_5,plain,
( ! [U_417,U_415,U_413] :
( U_413 = set_difference(U_417,U_415)
| ( ~ in(sK79(U_417,U_415,U_413),U_413)
& ~ in(sK79(U_417,U_415,U_413),U_415)
& in(sK79(U_417,U_415,U_413),U_417) )
| ( ( in(sK78(U_417,U_415,U_413),U_415)
| ~ in(sK78(U_417,U_415,U_413),U_417) )
& in(sK78(U_417,U_415,U_413),U_413) ) )
& ! [U_416,U_414,U_412] :
( ( ! [U_409] :
( in(U_409,U_412)
| in(U_409,U_414)
| ~ in(U_409,U_416) )
& ! [U_408] :
( ( ~ in(U_408,U_414)
& in(U_408,U_416) )
| ~ in(U_408,U_412) ) )
| U_412 != set_difference(U_416,U_414) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_411,sK79(U_417,U_415,U_413))],[f_51_4]) ).
cnf(f_51_6,plain,
( in(U_408,U_416)
| ~ in(U_408,U_412)
| U_412 != set_difference(U_416,U_414) ),
inference(clausify,[status(thm)],[f_51_5]) ).
cnf(f_51_7,plain,
( ~ in(U_408,U_414)
| ~ in(U_408,U_412)
| U_412 != set_difference(U_416,U_414) ),
inference(clausify,[status(thm)],[f_51_5]) ).
cnf(f_51_8,plain,
( in(U_409,U_412)
| in(U_409,U_414)
| ~ in(U_409,U_416)
| U_412 != set_difference(U_416,U_414) ),
inference(clausify,[status(thm)],[f_51_5]) ).
cnf(f_51_9,plain,
( in(sK79(U_417,U_415,U_413),U_417)
| in(sK78(U_417,U_415,U_413),U_413)
| U_413 = set_difference(U_417,U_415) ),
inference(clausify,[status(thm)],[f_51_5]) ).
cnf(f_51_10,plain,
( ~ in(sK79(U_417,U_415,U_413),U_415)
| in(sK78(U_417,U_415,U_413),U_413)
| U_413 = set_difference(U_417,U_415) ),
inference(clausify,[status(thm)],[f_51_5]) ).
cnf(f_51_11,plain,
( ~ in(sK79(U_417,U_415,U_413),U_413)
| in(sK78(U_417,U_415,U_413),U_413)
| U_413 = set_difference(U_417,U_415) ),
inference(clausify,[status(thm)],[f_51_5]) ).
cnf(f_51_12,plain,
( in(sK79(U_417,U_415,U_413),U_417)
| in(sK78(U_417,U_415,U_413),U_415)
| ~ in(sK78(U_417,U_415,U_413),U_417)
| U_413 = set_difference(U_417,U_415) ),
inference(clausify,[status(thm)],[f_51_5]) ).
cnf(f_51_13,plain,
( ~ in(sK79(U_417,U_415,U_413),U_415)
| in(sK78(U_417,U_415,U_413),U_415)
| ~ in(sK78(U_417,U_415,U_413),U_417)
| U_413 = set_difference(U_417,U_415) ),
inference(clausify,[status(thm)],[f_51_5]) ).
cnf(f_51_14,plain,
( ~ in(sK79(U_417,U_415,U_413),U_413)
| in(sK78(U_417,U_415,U_413),U_415)
| ~ in(sK78(U_417,U_415,U_413),U_417)
| U_413 = set_difference(U_417,U_415) ),
inference(clausify,[status(thm)],[f_51_5]) ).
fof(f_52_1,plain,
! [A] :
( ! [B] :
( ( B = relation_rng(A)
| ? [C] :
( ( ~ in(C,B)
& ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) )
| ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) ) )
& ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d5_funct_1]) ).
fof(f_52_2,plain,
! [U_425] :
( ! [U_424] :
( ( U_424 = relation_rng(U_425)
| ? [U_423] :
( ( ~ in(U_423,U_424)
& ? [U_422] :
( U_423 = apply(U_425,U_422)
& in(U_422,relation_dom(U_425)) ) )
| ( ! [U_421] :
( U_423 != apply(U_425,U_421)
| ~ in(U_421,relation_dom(U_425)) )
& in(U_423,U_424) ) ) )
& ( ! [U_420] :
( ( in(U_420,U_424)
| ! [U_419] :
( U_420 != apply(U_425,U_419)
| ~ in(U_419,relation_dom(U_425)) ) )
& ( ? [U_418] :
( U_420 = apply(U_425,U_418)
& in(U_418,relation_dom(U_425)) )
| ~ in(U_420,U_424) ) )
| U_424 != relation_rng(U_425) ) )
| ~ function(U_425)
| ~ relation(U_425) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
! [U_425] :
( ( ! [U_431] :
( U_431 = relation_rng(U_425)
| ? [U_429] :
( ~ in(U_429,U_431)
& ? [U_422] :
( U_429 = apply(U_425,U_422)
& in(U_422,relation_dom(U_425)) ) )
| ? [U_428] :
( ! [U_421] :
( U_428 != apply(U_425,U_421)
| ~ in(U_421,relation_dom(U_425)) )
& in(U_428,U_431) ) )
& ! [U_430] :
( ( ! [U_427] :
( in(U_427,U_430)
| ! [U_419] :
( U_427 != apply(U_425,U_419)
| ~ in(U_419,relation_dom(U_425)) ) )
& ! [U_426] :
( ? [U_418] :
( U_426 = apply(U_425,U_418)
& in(U_418,relation_dom(U_425)) )
| ~ in(U_426,U_430) ) )
| U_430 != relation_rng(U_425) ) )
| ~ function(U_425)
| ~ relation(U_425) ),
inference(miniscope,[status(thm)],[f_52_2]) ).
fof(f_52_4,plain,
! [U_425] :
( ( ! [U_431] :
( U_431 = relation_rng(U_425)
| ? [U_429] :
( ~ in(U_429,U_431)
& ? [U_422] :
( U_429 = apply(U_425,U_422)
& in(U_422,relation_dom(U_425)) ) )
| ? [U_428] :
( ! [U_421] :
( U_428 != apply(U_425,U_421)
| ~ in(U_421,relation_dom(U_425)) )
& in(U_428,U_431) ) )
& ! [U_430] :
( ( ! [U_427] :
( in(U_427,U_430)
| ! [U_419] :
( U_427 != apply(U_425,U_419)
| ~ in(U_419,relation_dom(U_425)) ) )
& ! [U_426] :
( ( U_426 = apply(U_425,sK80(U_425,U_430,U_426))
& in(sK80(U_425,U_430,U_426),relation_dom(U_425)) )
| ~ in(U_426,U_430) ) )
| U_430 != relation_rng(U_425) ) )
| ~ function(U_425)
| ~ relation(U_425) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_418,sK80(U_425,U_430,U_426))],[f_52_3]) ).
fof(f_52_5,plain,
! [U_425] :
( ( ! [U_431] :
( U_431 = relation_rng(U_425)
| ? [U_429] :
( ~ in(U_429,U_431)
& ? [U_422] :
( U_429 = apply(U_425,U_422)
& in(U_422,relation_dom(U_425)) ) )
| ( ! [U_421] :
( sK81(U_425,U_431) != apply(U_425,U_421)
| ~ in(U_421,relation_dom(U_425)) )
& in(sK81(U_425,U_431),U_431) ) )
& ! [U_430] :
( ( ! [U_427] :
( in(U_427,U_430)
| ! [U_419] :
( U_427 != apply(U_425,U_419)
| ~ in(U_419,relation_dom(U_425)) ) )
& ! [U_426] :
( ( U_426 = apply(U_425,sK80(U_425,U_430,U_426))
& in(sK80(U_425,U_430,U_426),relation_dom(U_425)) )
| ~ in(U_426,U_430) ) )
| U_430 != relation_rng(U_425) ) )
| ~ function(U_425)
| ~ relation(U_425) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_428,sK81(U_425,U_431))],[f_52_4]) ).
fof(f_52_6,plain,
! [U_425] :
( ( ! [U_431] :
( U_431 = relation_rng(U_425)
| ( ~ in(sK82(U_425,U_431),U_431)
& ? [U_422] :
( sK82(U_425,U_431) = apply(U_425,U_422)
& in(U_422,relation_dom(U_425)) ) )
| ( ! [U_421] :
( sK81(U_425,U_431) != apply(U_425,U_421)
| ~ in(U_421,relation_dom(U_425)) )
& in(sK81(U_425,U_431),U_431) ) )
& ! [U_430] :
( ( ! [U_427] :
( in(U_427,U_430)
| ! [U_419] :
( U_427 != apply(U_425,U_419)
| ~ in(U_419,relation_dom(U_425)) ) )
& ! [U_426] :
( ( U_426 = apply(U_425,sK80(U_425,U_430,U_426))
& in(sK80(U_425,U_430,U_426),relation_dom(U_425)) )
| ~ in(U_426,U_430) ) )
| U_430 != relation_rng(U_425) ) )
| ~ function(U_425)
| ~ relation(U_425) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_429,sK82(U_425,U_431))],[f_52_5]) ).
fof(f_52_7,plain,
! [U_425] :
( ( ! [U_431] :
( U_431 = relation_rng(U_425)
| ( ~ in(sK82(U_425,U_431),U_431)
& sK82(U_425,U_431) = apply(U_425,sK83(U_425,U_431))
& in(sK83(U_425,U_431),relation_dom(U_425)) )
| ( ! [U_421] :
( sK81(U_425,U_431) != apply(U_425,U_421)
| ~ in(U_421,relation_dom(U_425)) )
& in(sK81(U_425,U_431),U_431) ) )
& ! [U_430] :
( ( ! [U_427] :
( in(U_427,U_430)
| ! [U_419] :
( U_427 != apply(U_425,U_419)
| ~ in(U_419,relation_dom(U_425)) ) )
& ! [U_426] :
( ( U_426 = apply(U_425,sK80(U_425,U_430,U_426))
& in(sK80(U_425,U_430,U_426),relation_dom(U_425)) )
| ~ in(U_426,U_430) ) )
| U_430 != relation_rng(U_425) ) )
| ~ function(U_425)
| ~ relation(U_425) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_422,sK83(U_425,U_431))],[f_52_6]) ).
cnf(f_52_8,plain,
( in(sK80(U_425,U_430,U_426),relation_dom(U_425))
| ~ in(U_426,U_430)
| U_430 != relation_rng(U_425)
| ~ function(U_425)
| ~ relation(U_425) ),
inference(clausify,[status(thm)],[f_52_7]) ).
cnf(f_52_9,plain,
( U_426 = apply(U_425,sK80(U_425,U_430,U_426))
| ~ in(U_426,U_430)
| U_430 != relation_rng(U_425)
| ~ function(U_425)
| ~ relation(U_425) ),
inference(clausify,[status(thm)],[f_52_7]) ).
cnf(f_52_10,plain,
( in(U_427,U_430)
| U_427 != apply(U_425,U_419)
| ~ in(U_419,relation_dom(U_425))
| U_430 != relation_rng(U_425)
| ~ function(U_425)
| ~ relation(U_425) ),
inference(clausify,[status(thm)],[f_52_7]) ).
cnf(f_52_11,plain,
( in(sK83(U_425,U_431),relation_dom(U_425))
| in(sK81(U_425,U_431),U_431)
| U_431 = relation_rng(U_425)
| ~ function(U_425)
| ~ relation(U_425) ),
inference(clausify,[status(thm)],[f_52_7]) ).
cnf(f_52_12,plain,
( sK82(U_425,U_431) = apply(U_425,sK83(U_425,U_431))
| in(sK81(U_425,U_431),U_431)
| U_431 = relation_rng(U_425)
| ~ function(U_425)
| ~ relation(U_425) ),
inference(clausify,[status(thm)],[f_52_7]) ).
cnf(f_52_13,plain,
( ~ in(sK82(U_425,U_431),U_431)
| in(sK81(U_425,U_431),U_431)
| U_431 = relation_rng(U_425)
| ~ function(U_425)
| ~ relation(U_425) ),
inference(clausify,[status(thm)],[f_52_7]) ).
cnf(f_52_14,plain,
( in(sK83(U_425,U_431),relation_dom(U_425))
| sK81(U_425,U_431) != apply(U_425,U_421)
| ~ in(U_421,relation_dom(U_425))
| U_431 = relation_rng(U_425)
| ~ function(U_425)
| ~ relation(U_425) ),
inference(clausify,[status(thm)],[f_52_7]) ).
cnf(f_52_15,plain,
( sK82(U_425,U_431) = apply(U_425,sK83(U_425,U_431))
| sK81(U_425,U_431) != apply(U_425,U_421)
| ~ in(U_421,relation_dom(U_425))
| U_431 = relation_rng(U_425)
| ~ function(U_425)
| ~ relation(U_425) ),
inference(clausify,[status(thm)],[f_52_7]) ).
cnf(f_52_16,plain,
( ~ in(sK82(U_425,U_431),U_431)
| sK81(U_425,U_431) != apply(U_425,U_421)
| ~ in(U_421,relation_dom(U_425))
| U_431 = relation_rng(U_425)
| ~ function(U_425)
| ~ relation(U_425) ),
inference(clausify,[status(thm)],[f_52_7]) ).
fof(f_53_1,plain,
! [A] :
( ! [B] :
( ( B = relation_rng(A)
| ? [C] :
( ( ~ in(C,B)
& ? [D] : in(ordered_pair(D,C),A) )
| ( ! [D] : ~ in(ordered_pair(D,C),A)
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ! [D] : ~ in(ordered_pair(D,C),A) )
& ( ? [D] : in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d5_relat_1]) ).
fof(f_53_2,plain,
! [U_439] :
( ! [U_438] :
( ( U_438 = relation_rng(U_439)
| ? [U_437] :
( ( ~ in(U_437,U_438)
& ? [U_436] : in(ordered_pair(U_436,U_437),U_439) )
| ( ! [U_435] : ~ in(ordered_pair(U_435,U_437),U_439)
& in(U_437,U_438) ) ) )
& ( ! [U_434] :
( ( in(U_434,U_438)
| ! [U_433] : ~ in(ordered_pair(U_433,U_434),U_439) )
& ( ? [U_432] : in(ordered_pair(U_432,U_434),U_439)
| ~ in(U_434,U_438) ) )
| U_438 != relation_rng(U_439) ) )
| ~ relation(U_439) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
! [U_439] :
( ( ! [U_445] :
( U_445 = relation_rng(U_439)
| ? [U_443] :
( ~ in(U_443,U_445)
& ? [U_436] : in(ordered_pair(U_436,U_443),U_439) )
| ? [U_442] :
( ! [U_435] : ~ in(ordered_pair(U_435,U_442),U_439)
& in(U_442,U_445) ) )
& ! [U_444] :
( ( ! [U_441] :
( in(U_441,U_444)
| ! [U_433] : ~ in(ordered_pair(U_433,U_441),U_439) )
& ! [U_440] :
( ? [U_432] : in(ordered_pair(U_432,U_440),U_439)
| ~ in(U_440,U_444) ) )
| U_444 != relation_rng(U_439) ) )
| ~ relation(U_439) ),
inference(miniscope,[status(thm)],[f_53_2]) ).
fof(f_53_4,plain,
! [U_439] :
( ( ! [U_445] :
( U_445 = relation_rng(U_439)
| ? [U_443] :
( ~ in(U_443,U_445)
& ? [U_436] : in(ordered_pair(U_436,U_443),U_439) )
| ? [U_442] :
( ! [U_435] : ~ in(ordered_pair(U_435,U_442),U_439)
& in(U_442,U_445) ) )
& ! [U_444] :
( ( ! [U_441] :
( in(U_441,U_444)
| ! [U_433] : ~ in(ordered_pair(U_433,U_441),U_439) )
& ! [U_440] :
( in(ordered_pair(sK84(U_439,U_444,U_440),U_440),U_439)
| ~ in(U_440,U_444) ) )
| U_444 != relation_rng(U_439) ) )
| ~ relation(U_439) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_432,sK84(U_439,U_444,U_440))],[f_53_3]) ).
fof(f_53_5,plain,
! [U_439] :
( ( ! [U_445] :
( U_445 = relation_rng(U_439)
| ? [U_443] :
( ~ in(U_443,U_445)
& ? [U_436] : in(ordered_pair(U_436,U_443),U_439) )
| ( ! [U_435] : ~ in(ordered_pair(U_435,sK85(U_439,U_445)),U_439)
& in(sK85(U_439,U_445),U_445) ) )
& ! [U_444] :
( ( ! [U_441] :
( in(U_441,U_444)
| ! [U_433] : ~ in(ordered_pair(U_433,U_441),U_439) )
& ! [U_440] :
( in(ordered_pair(sK84(U_439,U_444,U_440),U_440),U_439)
| ~ in(U_440,U_444) ) )
| U_444 != relation_rng(U_439) ) )
| ~ relation(U_439) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_442,sK85(U_439,U_445))],[f_53_4]) ).
fof(f_53_6,plain,
! [U_439] :
( ( ! [U_445] :
( U_445 = relation_rng(U_439)
| ( ~ in(sK86(U_439,U_445),U_445)
& ? [U_436] : in(ordered_pair(U_436,sK86(U_439,U_445)),U_439) )
| ( ! [U_435] : ~ in(ordered_pair(U_435,sK85(U_439,U_445)),U_439)
& in(sK85(U_439,U_445),U_445) ) )
& ! [U_444] :
( ( ! [U_441] :
( in(U_441,U_444)
| ! [U_433] : ~ in(ordered_pair(U_433,U_441),U_439) )
& ! [U_440] :
( in(ordered_pair(sK84(U_439,U_444,U_440),U_440),U_439)
| ~ in(U_440,U_444) ) )
| U_444 != relation_rng(U_439) ) )
| ~ relation(U_439) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_443,sK86(U_439,U_445))],[f_53_5]) ).
fof(f_53_7,plain,
! [U_439] :
( ( ! [U_445] :
( U_445 = relation_rng(U_439)
| ( ~ in(sK86(U_439,U_445),U_445)
& in(ordered_pair(sK87(U_439,U_445),sK86(U_439,U_445)),U_439) )
| ( ! [U_435] : ~ in(ordered_pair(U_435,sK85(U_439,U_445)),U_439)
& in(sK85(U_439,U_445),U_445) ) )
& ! [U_444] :
( ( ! [U_441] :
( in(U_441,U_444)
| ! [U_433] : ~ in(ordered_pair(U_433,U_441),U_439) )
& ! [U_440] :
( in(ordered_pair(sK84(U_439,U_444,U_440),U_440),U_439)
| ~ in(U_440,U_444) ) )
| U_444 != relation_rng(U_439) ) )
| ~ relation(U_439) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_436,sK87(U_439,U_445))],[f_53_6]) ).
cnf(f_53_8,plain,
( in(ordered_pair(sK84(U_439,U_444,U_440),U_440),U_439)
| ~ in(U_440,U_444)
| U_444 != relation_rng(U_439)
| ~ relation(U_439) ),
inference(clausify,[status(thm)],[f_53_7]) ).
cnf(f_53_9,plain,
( in(U_441,U_444)
| ~ in(ordered_pair(U_433,U_441),U_439)
| U_444 != relation_rng(U_439)
| ~ relation(U_439) ),
inference(clausify,[status(thm)],[f_53_7]) ).
cnf(f_53_10,plain,
( in(ordered_pair(sK87(U_439,U_445),sK86(U_439,U_445)),U_439)
| in(sK85(U_439,U_445),U_445)
| U_445 = relation_rng(U_439)
| ~ relation(U_439) ),
inference(clausify,[status(thm)],[f_53_7]) ).
cnf(f_53_11,plain,
( ~ in(sK86(U_439,U_445),U_445)
| in(sK85(U_439,U_445),U_445)
| U_445 = relation_rng(U_439)
| ~ relation(U_439) ),
inference(clausify,[status(thm)],[f_53_7]) ).
cnf(f_53_12,plain,
( in(ordered_pair(sK87(U_439,U_445),sK86(U_439,U_445)),U_439)
| ~ in(ordered_pair(U_435,sK85(U_439,U_445)),U_439)
| U_445 = relation_rng(U_439)
| ~ relation(U_439) ),
inference(clausify,[status(thm)],[f_53_7]) ).
cnf(f_53_13,plain,
( ~ in(sK86(U_439,U_445),U_445)
| ~ in(ordered_pair(U_435,sK85(U_439,U_445)),U_439)
| U_445 = relation_rng(U_439)
| ~ relation(U_439) ),
inference(clausify,[status(thm)],[f_53_7]) ).
fof(f_54_1,plain,
! [A,B] :
( subset_complement(A,B) = set_difference(A,B)
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[d5_subset_1]) ).
fof(f_54_2,plain,
! [U_447,U_446] :
( subset_complement(U_447,U_446) = set_difference(U_447,U_446)
| ~ element(U_446,powerset(U_447)) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
cnf(f_54_3,plain,
( subset_complement(U_447,U_446) = set_difference(U_447,U_446)
| ~ element(U_446,powerset(U_447)) ),
inference(clausify,[status(thm)],[f_54_2]) ).
fof(f_55_1,plain,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(fof_nnf,[status(thm)],[d5_tarski]) ).
fof(f_55_2,plain,
! [U_449,U_448] : ordered_pair(U_449,U_448) = unordered_pair(unordered_pair(U_449,U_448),singleton(U_449)),
inference(variable_rename,[status(thm)],[f_55_1]) ).
cnf(f_55_3,plain,
ordered_pair(U_449,U_448) = unordered_pair(unordered_pair(U_449,U_448),singleton(U_449)),
inference(clausify,[status(thm)],[f_55_2]) ).
fof(f_56_1,plain,
! [A] :
( ! [B] :
( ( well_orders(A,B)
| ~ is_well_founded_in(A,B)
| ~ is_connected_in(A,B)
| ~ is_antisymmetric_in(A,B)
| ~ is_transitive_in(A,B)
| ~ is_reflexive_in(A,B) )
& ( ( is_well_founded_in(A,B)
& is_connected_in(A,B)
& is_antisymmetric_in(A,B)
& is_transitive_in(A,B)
& is_reflexive_in(A,B) )
| ~ well_orders(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d5_wellord1]) ).
fof(f_56_2,plain,
! [U_451] :
( ! [U_450] :
( ( well_orders(U_451,U_450)
| ~ is_well_founded_in(U_451,U_450)
| ~ is_connected_in(U_451,U_450)
| ~ is_antisymmetric_in(U_451,U_450)
| ~ is_transitive_in(U_451,U_450)
| ~ is_reflexive_in(U_451,U_450) )
& ( ( is_well_founded_in(U_451,U_450)
& is_connected_in(U_451,U_450)
& is_antisymmetric_in(U_451,U_450)
& is_transitive_in(U_451,U_450)
& is_reflexive_in(U_451,U_450) )
| ~ well_orders(U_451,U_450) ) )
| ~ relation(U_451) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
! [U_451] :
( ( ! [U_453] :
( well_orders(U_451,U_453)
| ~ is_well_founded_in(U_451,U_453)
| ~ is_connected_in(U_451,U_453)
| ~ is_antisymmetric_in(U_451,U_453)
| ~ is_transitive_in(U_451,U_453)
| ~ is_reflexive_in(U_451,U_453) )
& ! [U_452] :
( ( is_well_founded_in(U_451,U_452)
& is_connected_in(U_451,U_452)
& is_antisymmetric_in(U_451,U_452)
& is_transitive_in(U_451,U_452)
& is_reflexive_in(U_451,U_452) )
| ~ well_orders(U_451,U_452) ) )
| ~ relation(U_451) ),
inference(miniscope,[status(thm)],[f_56_2]) ).
cnf(f_56_4,plain,
( is_reflexive_in(U_451,U_452)
| ~ well_orders(U_451,U_452)
| ~ relation(U_451) ),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_5,plain,
( is_transitive_in(U_451,U_452)
| ~ well_orders(U_451,U_452)
| ~ relation(U_451) ),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_6,plain,
( is_antisymmetric_in(U_451,U_452)
| ~ well_orders(U_451,U_452)
| ~ relation(U_451) ),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_7,plain,
( is_connected_in(U_451,U_452)
| ~ well_orders(U_451,U_452)
| ~ relation(U_451) ),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_8,plain,
( is_well_founded_in(U_451,U_452)
| ~ well_orders(U_451,U_452)
| ~ relation(U_451) ),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_9,plain,
( well_orders(U_451,U_453)
| ~ is_well_founded_in(U_451,U_453)
| ~ is_connected_in(U_451,U_453)
| ~ is_antisymmetric_in(U_451,U_453)
| ~ is_transitive_in(U_451,U_453)
| ~ is_reflexive_in(U_451,U_453)
| ~ relation(U_451) ),
inference(clausify,[status(thm)],[f_56_3]) ).
fof(f_57_1,plain,
! [A] :
( ( being_limit_ordinal(A)
| A != union(A) )
& ( A = union(A)
| ~ being_limit_ordinal(A) ) ),
inference(fof_nnf,[status(thm)],[d6_ordinal1]) ).
fof(f_57_2,plain,
! [U_454] :
( ( being_limit_ordinal(U_454)
| U_454 != union(U_454) )
& ( U_454 = union(U_454)
| ~ being_limit_ordinal(U_454) ) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
( ! [U_456] :
( being_limit_ordinal(U_456)
| U_456 != union(U_456) )
& ! [U_455] :
( U_455 = union(U_455)
| ~ being_limit_ordinal(U_455) ) ),
inference(miniscope,[status(thm)],[f_57_2]) ).
cnf(f_57_4,plain,
( U_455 = union(U_455)
| ~ being_limit_ordinal(U_455) ),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_5,plain,
( being_limit_ordinal(U_456)
| U_456 != union(U_456) ),
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_1,plain,
! [A] :
( relation_field(A) = set_union2(relation_dom(A),relation_rng(A))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d6_relat_1]) ).
fof(f_58_2,plain,
! [U_457] :
( relation_field(U_457) = set_union2(relation_dom(U_457),relation_rng(U_457))
| ~ relation(U_457) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
cnf(f_58_3,plain,
( relation_field(U_457) = set_union2(relation_dom(U_457),relation_rng(U_457))
| ~ relation(U_457) ),
inference(clausify,[status(thm)],[f_58_2]) ).
fof(f_59_1,plain,
! [A] :
( ! [B] :
( ( is_connected_in(A,B)
| ? [C,D] :
( ~ in(ordered_pair(D,C),A)
& ~ in(ordered_pair(C,D),A)
& C != D
& in(D,B)
& in(C,B) ) )
& ( ! [C,D] :
( in(ordered_pair(D,C),A)
| in(ordered_pair(C,D),A)
| C = D
| ~ in(D,B)
| ~ in(C,B) )
| ~ is_connected_in(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d6_relat_2]) ).
fof(f_59_2,plain,
! [U_463] :
( ! [U_462] :
( ( is_connected_in(U_463,U_462)
| ? [U_461,U_460] :
( ~ in(ordered_pair(U_460,U_461),U_463)
& ~ in(ordered_pair(U_461,U_460),U_463)
& U_461 != U_460
& in(U_460,U_462)
& in(U_461,U_462) ) )
& ( ! [U_459,U_458] :
( in(ordered_pair(U_458,U_459),U_463)
| in(ordered_pair(U_459,U_458),U_463)
| U_459 = U_458
| ~ in(U_458,U_462)
| ~ in(U_459,U_462) )
| ~ is_connected_in(U_463,U_462) ) )
| ~ relation(U_463) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
! [U_463] :
( ( ! [U_465] :
( is_connected_in(U_463,U_465)
| ? [U_461] :
( ? [U_460] :
( ~ in(ordered_pair(U_460,U_461),U_463)
& ~ in(ordered_pair(U_461,U_460),U_463)
& U_461 != U_460
& in(U_460,U_465) )
& in(U_461,U_465) ) )
& ! [U_464] :
( ! [U_459] :
( ! [U_458] :
( in(ordered_pair(U_458,U_459),U_463)
| in(ordered_pair(U_459,U_458),U_463)
| U_459 = U_458
| ~ in(U_458,U_464) )
| ~ in(U_459,U_464) )
| ~ is_connected_in(U_463,U_464) ) )
| ~ relation(U_463) ),
inference(miniscope,[status(thm)],[f_59_2]) ).
fof(f_59_4,plain,
! [U_463] :
( ( ! [U_465] :
( is_connected_in(U_463,U_465)
| ( ? [U_460] :
( ~ in(ordered_pair(U_460,sK88(U_463,U_465)),U_463)
& ~ in(ordered_pair(sK88(U_463,U_465),U_460),U_463)
& sK88(U_463,U_465) != U_460
& in(U_460,U_465) )
& in(sK88(U_463,U_465),U_465) ) )
& ! [U_464] :
( ! [U_459] :
( ! [U_458] :
( in(ordered_pair(U_458,U_459),U_463)
| in(ordered_pair(U_459,U_458),U_463)
| U_459 = U_458
| ~ in(U_458,U_464) )
| ~ in(U_459,U_464) )
| ~ is_connected_in(U_463,U_464) ) )
| ~ relation(U_463) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_461,sK88(U_463,U_465))],[f_59_3]) ).
fof(f_59_5,plain,
! [U_463] :
( ( ! [U_465] :
( is_connected_in(U_463,U_465)
| ( ~ in(ordered_pair(sK89(U_463,U_465),sK88(U_463,U_465)),U_463)
& ~ in(ordered_pair(sK88(U_463,U_465),sK89(U_463,U_465)),U_463)
& sK88(U_463,U_465) != sK89(U_463,U_465)
& in(sK89(U_463,U_465),U_465)
& in(sK88(U_463,U_465),U_465) ) )
& ! [U_464] :
( ! [U_459] :
( ! [U_458] :
( in(ordered_pair(U_458,U_459),U_463)
| in(ordered_pair(U_459,U_458),U_463)
| U_459 = U_458
| ~ in(U_458,U_464) )
| ~ in(U_459,U_464) )
| ~ is_connected_in(U_463,U_464) ) )
| ~ relation(U_463) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_460,sK89(U_463,U_465))],[f_59_4]) ).
cnf(f_59_6,plain,
( in(ordered_pair(U_458,U_459),U_463)
| in(ordered_pair(U_459,U_458),U_463)
| U_459 = U_458
| ~ in(U_458,U_464)
| ~ in(U_459,U_464)
| ~ is_connected_in(U_463,U_464)
| ~ relation(U_463) ),
inference(clausify,[status(thm)],[f_59_5]) ).
cnf(f_59_7,plain,
( in(sK88(U_463,U_465),U_465)
| is_connected_in(U_463,U_465)
| ~ relation(U_463) ),
inference(clausify,[status(thm)],[f_59_5]) ).
cnf(f_59_8,plain,
( in(sK89(U_463,U_465),U_465)
| is_connected_in(U_463,U_465)
| ~ relation(U_463) ),
inference(clausify,[status(thm)],[f_59_5]) ).
cnf(f_59_9,plain,
( sK88(U_463,U_465) != sK89(U_463,U_465)
| is_connected_in(U_463,U_465)
| ~ relation(U_463) ),
inference(clausify,[status(thm)],[f_59_5]) ).
cnf(f_59_10,plain,
( ~ in(ordered_pair(sK88(U_463,U_465),sK89(U_463,U_465)),U_463)
| is_connected_in(U_463,U_465)
| ~ relation(U_463) ),
inference(clausify,[status(thm)],[f_59_5]) ).
cnf(f_59_11,plain,
( ~ in(ordered_pair(sK89(U_463,U_465),sK88(U_463,U_465)),U_463)
| is_connected_in(U_463,U_465)
| ~ relation(U_463) ),
inference(clausify,[status(thm)],[f_59_5]) ).
fof(f_60_1,plain,
! [A] :
( ! [B] :
( ( ( B = relation_inverse(A)
| ? [C,D] :
( ( ~ in(ordered_pair(C,D),B)
& in(ordered_pair(D,C),A) )
| ( ~ in(ordered_pair(D,C),A)
& in(ordered_pair(C,D),B) ) ) )
& ( ! [C,D] :
( ( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(D,C),A) )
& ( in(ordered_pair(D,C),A)
| ~ in(ordered_pair(C,D),B) ) )
| B != relation_inverse(A) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d7_relat_1]) ).
fof(f_60_2,plain,
! [U_471] :
( ! [U_470] :
( ( ( U_470 = relation_inverse(U_471)
| ? [U_469,U_468] :
( ( ~ in(ordered_pair(U_469,U_468),U_470)
& in(ordered_pair(U_468,U_469),U_471) )
| ( ~ in(ordered_pair(U_468,U_469),U_471)
& in(ordered_pair(U_469,U_468),U_470) ) ) )
& ( ! [U_467,U_466] :
( ( in(ordered_pair(U_467,U_466),U_470)
| ~ in(ordered_pair(U_466,U_467),U_471) )
& ( in(ordered_pair(U_466,U_467),U_471)
| ~ in(ordered_pair(U_467,U_466),U_470) ) )
| U_470 != relation_inverse(U_471) ) )
| ~ relation(U_470) )
| ~ relation(U_471) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
! [U_471] :
( ! [U_470] :
( ( ( U_470 = relation_inverse(U_471)
| ? [U_479,U_477] :
( ~ in(ordered_pair(U_479,U_477),U_470)
& in(ordered_pair(U_477,U_479),U_471) )
| ? [U_478,U_476] :
( ~ in(ordered_pair(U_476,U_478),U_471)
& in(ordered_pair(U_478,U_476),U_470) ) )
& ( ( ! [U_475,U_473] :
( in(ordered_pair(U_475,U_473),U_470)
| ~ in(ordered_pair(U_473,U_475),U_471) )
& ! [U_474,U_472] :
( in(ordered_pair(U_472,U_474),U_471)
| ~ in(ordered_pair(U_474,U_472),U_470) ) )
| U_470 != relation_inverse(U_471) ) )
| ~ relation(U_470) )
| ~ relation(U_471) ),
inference(miniscope,[status(thm)],[f_60_2]) ).
fof(f_60_4,plain,
! [U_471] :
( ! [U_470] :
( ( ( U_470 = relation_inverse(U_471)
| ? [U_479,U_477] :
( ~ in(ordered_pair(U_479,U_477),U_470)
& in(ordered_pair(U_477,U_479),U_471) )
| ? [U_476] :
( ~ in(ordered_pair(U_476,sK90(U_471,U_470)),U_471)
& in(ordered_pair(sK90(U_471,U_470),U_476),U_470) ) )
& ( ( ! [U_475,U_473] :
( in(ordered_pair(U_475,U_473),U_470)
| ~ in(ordered_pair(U_473,U_475),U_471) )
& ! [U_474,U_472] :
( in(ordered_pair(U_472,U_474),U_471)
| ~ in(ordered_pair(U_474,U_472),U_470) ) )
| U_470 != relation_inverse(U_471) ) )
| ~ relation(U_470) )
| ~ relation(U_471) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_478,sK90(U_471,U_470))],[f_60_3]) ).
fof(f_60_5,plain,
! [U_471] :
( ! [U_470] :
( ( ( U_470 = relation_inverse(U_471)
| ? [U_479,U_477] :
( ~ in(ordered_pair(U_479,U_477),U_470)
& in(ordered_pair(U_477,U_479),U_471) )
| ( ~ in(ordered_pair(sK91(U_471,U_470),sK90(U_471,U_470)),U_471)
& in(ordered_pair(sK90(U_471,U_470),sK91(U_471,U_470)),U_470) ) )
& ( ( ! [U_475,U_473] :
( in(ordered_pair(U_475,U_473),U_470)
| ~ in(ordered_pair(U_473,U_475),U_471) )
& ! [U_474,U_472] :
( in(ordered_pair(U_472,U_474),U_471)
| ~ in(ordered_pair(U_474,U_472),U_470) ) )
| U_470 != relation_inverse(U_471) ) )
| ~ relation(U_470) )
| ~ relation(U_471) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_476,sK91(U_471,U_470))],[f_60_4]) ).
fof(f_60_6,plain,
! [U_471] :
( ! [U_470] :
( ( ( U_470 = relation_inverse(U_471)
| ? [U_477] :
( ~ in(ordered_pair(sK92(U_471,U_470),U_477),U_470)
& in(ordered_pair(U_477,sK92(U_471,U_470)),U_471) )
| ( ~ in(ordered_pair(sK91(U_471,U_470),sK90(U_471,U_470)),U_471)
& in(ordered_pair(sK90(U_471,U_470),sK91(U_471,U_470)),U_470) ) )
& ( ( ! [U_475,U_473] :
( in(ordered_pair(U_475,U_473),U_470)
| ~ in(ordered_pair(U_473,U_475),U_471) )
& ! [U_474,U_472] :
( in(ordered_pair(U_472,U_474),U_471)
| ~ in(ordered_pair(U_474,U_472),U_470) ) )
| U_470 != relation_inverse(U_471) ) )
| ~ relation(U_470) )
| ~ relation(U_471) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_479,sK92(U_471,U_470))],[f_60_5]) ).
fof(f_60_7,plain,
! [U_471] :
( ! [U_470] :
( ( ( U_470 = relation_inverse(U_471)
| ( ~ in(ordered_pair(sK92(U_471,U_470),sK93(U_471,U_470)),U_470)
& in(ordered_pair(sK93(U_471,U_470),sK92(U_471,U_470)),U_471) )
| ( ~ in(ordered_pair(sK91(U_471,U_470),sK90(U_471,U_470)),U_471)
& in(ordered_pair(sK90(U_471,U_470),sK91(U_471,U_470)),U_470) ) )
& ( ( ! [U_475,U_473] :
( in(ordered_pair(U_475,U_473),U_470)
| ~ in(ordered_pair(U_473,U_475),U_471) )
& ! [U_474,U_472] :
( in(ordered_pair(U_472,U_474),U_471)
| ~ in(ordered_pair(U_474,U_472),U_470) ) )
| U_470 != relation_inverse(U_471) ) )
| ~ relation(U_470) )
| ~ relation(U_471) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_477,sK93(U_471,U_470))],[f_60_6]) ).
cnf(f_60_8,plain,
( in(ordered_pair(U_472,U_474),U_471)
| ~ in(ordered_pair(U_474,U_472),U_470)
| U_470 != relation_inverse(U_471)
| ~ relation(U_470)
| ~ relation(U_471) ),
inference(clausify,[status(thm)],[f_60_7]) ).
cnf(f_60_9,plain,
( in(ordered_pair(U_475,U_473),U_470)
| ~ in(ordered_pair(U_473,U_475),U_471)
| U_470 != relation_inverse(U_471)
| ~ relation(U_470)
| ~ relation(U_471) ),
inference(clausify,[status(thm)],[f_60_7]) ).
cnf(f_60_10,plain,
( in(ordered_pair(sK93(U_471,U_470),sK92(U_471,U_470)),U_471)
| in(ordered_pair(sK90(U_471,U_470),sK91(U_471,U_470)),U_470)
| U_470 = relation_inverse(U_471)
| ~ relation(U_470)
| ~ relation(U_471) ),
inference(clausify,[status(thm)],[f_60_7]) ).
cnf(f_60_11,plain,
( ~ in(ordered_pair(sK92(U_471,U_470),sK93(U_471,U_470)),U_470)
| in(ordered_pair(sK90(U_471,U_470),sK91(U_471,U_470)),U_470)
| U_470 = relation_inverse(U_471)
| ~ relation(U_470)
| ~ relation(U_471) ),
inference(clausify,[status(thm)],[f_60_7]) ).
cnf(f_60_12,plain,
( in(ordered_pair(sK93(U_471,U_470),sK92(U_471,U_470)),U_471)
| ~ in(ordered_pair(sK91(U_471,U_470),sK90(U_471,U_470)),U_471)
| U_470 = relation_inverse(U_471)
| ~ relation(U_470)
| ~ relation(U_471) ),
inference(clausify,[status(thm)],[f_60_7]) ).
cnf(f_60_13,plain,
( ~ in(ordered_pair(sK92(U_471,U_470),sK93(U_471,U_470)),U_470)
| ~ in(ordered_pair(sK91(U_471,U_470),sK90(U_471,U_470)),U_471)
| U_470 = relation_inverse(U_471)
| ~ relation(U_470)
| ~ relation(U_471) ),
inference(clausify,[status(thm)],[f_60_7]) ).
fof(f_61_1,plain,
! [A,B] :
( ( disjoint(A,B)
| set_intersection2(A,B) != empty_set )
& ( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[d7_xboole_0]) ).
fof(f_61_2,plain,
! [U_481,U_480] :
( ( disjoint(U_481,U_480)
| set_intersection2(U_481,U_480) != empty_set )
& ( set_intersection2(U_481,U_480) = empty_set
| ~ disjoint(U_481,U_480) ) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
( ! [U_485,U_483] :
( disjoint(U_485,U_483)
| set_intersection2(U_485,U_483) != empty_set )
& ! [U_484,U_482] :
( set_intersection2(U_484,U_482) = empty_set
| ~ disjoint(U_484,U_482) ) ),
inference(miniscope,[status(thm)],[f_61_2]) ).
cnf(f_61_4,plain,
( set_intersection2(U_484,U_482) = empty_set
| ~ disjoint(U_484,U_482) ),
inference(clausify,[status(thm)],[f_61_3]) ).
cnf(f_61_5,plain,
( disjoint(U_485,U_483)
| set_intersection2(U_485,U_483) != empty_set ),
inference(clausify,[status(thm)],[f_61_3]) ).
fof(f_62_1,plain,
! [A] :
( ( ( one_to_one(A)
| ? [B,C] :
( B != C
& apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) ) )
& ( ! [B,C] :
( B = C
| apply(A,B) != apply(A,C)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d8_funct_1]) ).
fof(f_62_2,plain,
! [U_490] :
( ( ( one_to_one(U_490)
| ? [U_489,U_488] :
( U_489 != U_488
& apply(U_490,U_489) = apply(U_490,U_488)
& in(U_488,relation_dom(U_490))
& in(U_489,relation_dom(U_490)) ) )
& ( ! [U_487,U_486] :
( U_487 = U_486
| apply(U_490,U_487) != apply(U_490,U_486)
| ~ in(U_486,relation_dom(U_490))
| ~ in(U_487,relation_dom(U_490)) )
| ~ one_to_one(U_490) ) )
| ~ function(U_490)
| ~ relation(U_490) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
! [U_490] :
( ( ( one_to_one(U_490)
| ? [U_488] :
( sK94(U_490) != U_488
& apply(U_490,sK94(U_490)) = apply(U_490,U_488)
& in(U_488,relation_dom(U_490))
& in(sK94(U_490),relation_dom(U_490)) ) )
& ( ! [U_487,U_486] :
( U_487 = U_486
| apply(U_490,U_487) != apply(U_490,U_486)
| ~ in(U_486,relation_dom(U_490))
| ~ in(U_487,relation_dom(U_490)) )
| ~ one_to_one(U_490) ) )
| ~ function(U_490)
| ~ relation(U_490) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_489,sK94(U_490))],[f_62_2]) ).
fof(f_62_4,plain,
! [U_490] :
( ( ( one_to_one(U_490)
| ( sK94(U_490) != sK95(U_490)
& apply(U_490,sK94(U_490)) = apply(U_490,sK95(U_490))
& in(sK95(U_490),relation_dom(U_490))
& in(sK94(U_490),relation_dom(U_490)) ) )
& ( ! [U_487,U_486] :
( U_487 = U_486
| apply(U_490,U_487) != apply(U_490,U_486)
| ~ in(U_486,relation_dom(U_490))
| ~ in(U_487,relation_dom(U_490)) )
| ~ one_to_one(U_490) ) )
| ~ function(U_490)
| ~ relation(U_490) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_488,sK95(U_490))],[f_62_3]) ).
cnf(f_62_5,plain,
( U_487 = U_486
| apply(U_490,U_487) != apply(U_490,U_486)
| ~ in(U_486,relation_dom(U_490))
| ~ in(U_487,relation_dom(U_490))
| ~ one_to_one(U_490)
| ~ function(U_490)
| ~ relation(U_490) ),
inference(clausify,[status(thm)],[f_62_4]) ).
cnf(f_62_6,plain,
( in(sK94(U_490),relation_dom(U_490))
| one_to_one(U_490)
| ~ function(U_490)
| ~ relation(U_490) ),
inference(clausify,[status(thm)],[f_62_4]) ).
cnf(f_62_7,plain,
( in(sK95(U_490),relation_dom(U_490))
| one_to_one(U_490)
| ~ function(U_490)
| ~ relation(U_490) ),
inference(clausify,[status(thm)],[f_62_4]) ).
cnf(f_62_8,plain,
( apply(U_490,sK94(U_490)) = apply(U_490,sK95(U_490))
| one_to_one(U_490)
| ~ function(U_490)
| ~ relation(U_490) ),
inference(clausify,[status(thm)],[f_62_4]) ).
cnf(f_62_9,plain,
( sK94(U_490) != sK95(U_490)
| one_to_one(U_490)
| ~ function(U_490)
| ~ relation(U_490) ),
inference(clausify,[status(thm)],[f_62_4]) ).
fof(f_63_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( C = relation_composition(A,B)
| ? [D,E] :
( ( ~ in(ordered_pair(D,E),C)
& ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) ) )
| ( ! [F] :
( ~ in(ordered_pair(F,E),B)
| ~ in(ordered_pair(D,F),A) )
& in(ordered_pair(D,E),C) ) ) )
& ( ! [D,E] :
( ( in(ordered_pair(D,E),C)
| ! [F] :
( ~ in(ordered_pair(F,E),B)
| ~ in(ordered_pair(D,F),A) ) )
& ( ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_composition(A,B) ) )
| ~ relation(C) )
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d8_relat_1]) ).
fof(f_63_2,plain,
! [U_501] :
( ! [U_500] :
( ! [U_499] :
( ( ( U_499 = relation_composition(U_501,U_500)
| ? [U_498,U_497] :
( ( ~ in(ordered_pair(U_498,U_497),U_499)
& ? [U_496] :
( in(ordered_pair(U_496,U_497),U_500)
& in(ordered_pair(U_498,U_496),U_501) ) )
| ( ! [U_495] :
( ~ in(ordered_pair(U_495,U_497),U_500)
| ~ in(ordered_pair(U_498,U_495),U_501) )
& in(ordered_pair(U_498,U_497),U_499) ) ) )
& ( ! [U_494,U_493] :
( ( in(ordered_pair(U_494,U_493),U_499)
| ! [U_492] :
( ~ in(ordered_pair(U_492,U_493),U_500)
| ~ in(ordered_pair(U_494,U_492),U_501) ) )
& ( ? [U_491] :
( in(ordered_pair(U_491,U_493),U_500)
& in(ordered_pair(U_494,U_491),U_501) )
| ~ in(ordered_pair(U_494,U_493),U_499) ) )
| U_499 != relation_composition(U_501,U_500) ) )
| ~ relation(U_499) )
| ~ relation(U_500) )
| ~ relation(U_501) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
! [U_501] :
( ! [U_500] :
( ! [U_499] :
( ( ( U_499 = relation_composition(U_501,U_500)
| ? [U_509,U_507] :
( ~ in(ordered_pair(U_509,U_507),U_499)
& ? [U_496] :
( in(ordered_pair(U_496,U_507),U_500)
& in(ordered_pair(U_509,U_496),U_501) ) )
| ? [U_508,U_506] :
( ! [U_495] :
( ~ in(ordered_pair(U_495,U_506),U_500)
| ~ in(ordered_pair(U_508,U_495),U_501) )
& in(ordered_pair(U_508,U_506),U_499) ) )
& ( ( ! [U_505,U_503] :
( in(ordered_pair(U_505,U_503),U_499)
| ! [U_492] :
( ~ in(ordered_pair(U_492,U_503),U_500)
| ~ in(ordered_pair(U_505,U_492),U_501) ) )
& ! [U_504,U_502] :
( ? [U_491] :
( in(ordered_pair(U_491,U_502),U_500)
& in(ordered_pair(U_504,U_491),U_501) )
| ~ in(ordered_pair(U_504,U_502),U_499) ) )
| U_499 != relation_composition(U_501,U_500) ) )
| ~ relation(U_499) )
| ~ relation(U_500) )
| ~ relation(U_501) ),
inference(miniscope,[status(thm)],[f_63_2]) ).
fof(f_63_4,plain,
! [U_501] :
( ! [U_500] :
( ! [U_499] :
( ( ( U_499 = relation_composition(U_501,U_500)
| ? [U_509,U_507] :
( ~ in(ordered_pair(U_509,U_507),U_499)
& ? [U_496] :
( in(ordered_pair(U_496,U_507),U_500)
& in(ordered_pair(U_509,U_496),U_501) ) )
| ? [U_508,U_506] :
( ! [U_495] :
( ~ in(ordered_pair(U_495,U_506),U_500)
| ~ in(ordered_pair(U_508,U_495),U_501) )
& in(ordered_pair(U_508,U_506),U_499) ) )
& ( ( ! [U_505,U_503] :
( in(ordered_pair(U_505,U_503),U_499)
| ! [U_492] :
( ~ in(ordered_pair(U_492,U_503),U_500)
| ~ in(ordered_pair(U_505,U_492),U_501) ) )
& ! [U_504,U_502] :
( ( in(ordered_pair(sK96(U_501,U_500,U_499,U_504,U_502),U_502),U_500)
& in(ordered_pair(U_504,sK96(U_501,U_500,U_499,U_504,U_502)),U_501) )
| ~ in(ordered_pair(U_504,U_502),U_499) ) )
| U_499 != relation_composition(U_501,U_500) ) )
| ~ relation(U_499) )
| ~ relation(U_500) )
| ~ relation(U_501) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_491,sK96(U_501,U_500,U_499,U_504,U_502))],[f_63_3]) ).
fof(f_63_5,plain,
! [U_501] :
( ! [U_500] :
( ! [U_499] :
( ( ( U_499 = relation_composition(U_501,U_500)
| ? [U_509,U_507] :
( ~ in(ordered_pair(U_509,U_507),U_499)
& ? [U_496] :
( in(ordered_pair(U_496,U_507),U_500)
& in(ordered_pair(U_509,U_496),U_501) ) )
| ? [U_506] :
( ! [U_495] :
( ~ in(ordered_pair(U_495,U_506),U_500)
| ~ in(ordered_pair(sK97(U_501,U_500,U_499),U_495),U_501) )
& in(ordered_pair(sK97(U_501,U_500,U_499),U_506),U_499) ) )
& ( ( ! [U_505,U_503] :
( in(ordered_pair(U_505,U_503),U_499)
| ! [U_492] :
( ~ in(ordered_pair(U_492,U_503),U_500)
| ~ in(ordered_pair(U_505,U_492),U_501) ) )
& ! [U_504,U_502] :
( ( in(ordered_pair(sK96(U_501,U_500,U_499,U_504,U_502),U_502),U_500)
& in(ordered_pair(U_504,sK96(U_501,U_500,U_499,U_504,U_502)),U_501) )
| ~ in(ordered_pair(U_504,U_502),U_499) ) )
| U_499 != relation_composition(U_501,U_500) ) )
| ~ relation(U_499) )
| ~ relation(U_500) )
| ~ relation(U_501) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_508,sK97(U_501,U_500,U_499))],[f_63_4]) ).
fof(f_63_6,plain,
! [U_501] :
( ! [U_500] :
( ! [U_499] :
( ( ( U_499 = relation_composition(U_501,U_500)
| ? [U_509,U_507] :
( ~ in(ordered_pair(U_509,U_507),U_499)
& ? [U_496] :
( in(ordered_pair(U_496,U_507),U_500)
& in(ordered_pair(U_509,U_496),U_501) ) )
| ( ! [U_495] :
( ~ in(ordered_pair(U_495,sK98(U_501,U_500,U_499)),U_500)
| ~ in(ordered_pair(sK97(U_501,U_500,U_499),U_495),U_501) )
& in(ordered_pair(sK97(U_501,U_500,U_499),sK98(U_501,U_500,U_499)),U_499) ) )
& ( ( ! [U_505,U_503] :
( in(ordered_pair(U_505,U_503),U_499)
| ! [U_492] :
( ~ in(ordered_pair(U_492,U_503),U_500)
| ~ in(ordered_pair(U_505,U_492),U_501) ) )
& ! [U_504,U_502] :
( ( in(ordered_pair(sK96(U_501,U_500,U_499,U_504,U_502),U_502),U_500)
& in(ordered_pair(U_504,sK96(U_501,U_500,U_499,U_504,U_502)),U_501) )
| ~ in(ordered_pair(U_504,U_502),U_499) ) )
| U_499 != relation_composition(U_501,U_500) ) )
| ~ relation(U_499) )
| ~ relation(U_500) )
| ~ relation(U_501) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_506,sK98(U_501,U_500,U_499))],[f_63_5]) ).
fof(f_63_7,plain,
! [U_501] :
( ! [U_500] :
( ! [U_499] :
( ( ( U_499 = relation_composition(U_501,U_500)
| ? [U_507] :
( ~ in(ordered_pair(sK99(U_501,U_500,U_499),U_507),U_499)
& ? [U_496] :
( in(ordered_pair(U_496,U_507),U_500)
& in(ordered_pair(sK99(U_501,U_500,U_499),U_496),U_501) ) )
| ( ! [U_495] :
( ~ in(ordered_pair(U_495,sK98(U_501,U_500,U_499)),U_500)
| ~ in(ordered_pair(sK97(U_501,U_500,U_499),U_495),U_501) )
& in(ordered_pair(sK97(U_501,U_500,U_499),sK98(U_501,U_500,U_499)),U_499) ) )
& ( ( ! [U_505,U_503] :
( in(ordered_pair(U_505,U_503),U_499)
| ! [U_492] :
( ~ in(ordered_pair(U_492,U_503),U_500)
| ~ in(ordered_pair(U_505,U_492),U_501) ) )
& ! [U_504,U_502] :
( ( in(ordered_pair(sK96(U_501,U_500,U_499,U_504,U_502),U_502),U_500)
& in(ordered_pair(U_504,sK96(U_501,U_500,U_499,U_504,U_502)),U_501) )
| ~ in(ordered_pair(U_504,U_502),U_499) ) )
| U_499 != relation_composition(U_501,U_500) ) )
| ~ relation(U_499) )
| ~ relation(U_500) )
| ~ relation(U_501) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_509,sK99(U_501,U_500,U_499))],[f_63_6]) ).
fof(f_63_8,plain,
! [U_501] :
( ! [U_500] :
( ! [U_499] :
( ( ( U_499 = relation_composition(U_501,U_500)
| ( ~ in(ordered_pair(sK99(U_501,U_500,U_499),sK100(U_501,U_500,U_499)),U_499)
& ? [U_496] :
( in(ordered_pair(U_496,sK100(U_501,U_500,U_499)),U_500)
& in(ordered_pair(sK99(U_501,U_500,U_499),U_496),U_501) ) )
| ( ! [U_495] :
( ~ in(ordered_pair(U_495,sK98(U_501,U_500,U_499)),U_500)
| ~ in(ordered_pair(sK97(U_501,U_500,U_499),U_495),U_501) )
& in(ordered_pair(sK97(U_501,U_500,U_499),sK98(U_501,U_500,U_499)),U_499) ) )
& ( ( ! [U_505,U_503] :
( in(ordered_pair(U_505,U_503),U_499)
| ! [U_492] :
( ~ in(ordered_pair(U_492,U_503),U_500)
| ~ in(ordered_pair(U_505,U_492),U_501) ) )
& ! [U_504,U_502] :
( ( in(ordered_pair(sK96(U_501,U_500,U_499,U_504,U_502),U_502),U_500)
& in(ordered_pair(U_504,sK96(U_501,U_500,U_499,U_504,U_502)),U_501) )
| ~ in(ordered_pair(U_504,U_502),U_499) ) )
| U_499 != relation_composition(U_501,U_500) ) )
| ~ relation(U_499) )
| ~ relation(U_500) )
| ~ relation(U_501) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_507,sK100(U_501,U_500,U_499))],[f_63_7]) ).
fof(f_63_9,plain,
! [U_501] :
( ! [U_500] :
( ! [U_499] :
( ( ( U_499 = relation_composition(U_501,U_500)
| ( ~ in(ordered_pair(sK99(U_501,U_500,U_499),sK100(U_501,U_500,U_499)),U_499)
& in(ordered_pair(sK101(U_501,U_500,U_499),sK100(U_501,U_500,U_499)),U_500)
& in(ordered_pair(sK99(U_501,U_500,U_499),sK101(U_501,U_500,U_499)),U_501) )
| ( ! [U_495] :
( ~ in(ordered_pair(U_495,sK98(U_501,U_500,U_499)),U_500)
| ~ in(ordered_pair(sK97(U_501,U_500,U_499),U_495),U_501) )
& in(ordered_pair(sK97(U_501,U_500,U_499),sK98(U_501,U_500,U_499)),U_499) ) )
& ( ( ! [U_505,U_503] :
( in(ordered_pair(U_505,U_503),U_499)
| ! [U_492] :
( ~ in(ordered_pair(U_492,U_503),U_500)
| ~ in(ordered_pair(U_505,U_492),U_501) ) )
& ! [U_504,U_502] :
( ( in(ordered_pair(sK96(U_501,U_500,U_499,U_504,U_502),U_502),U_500)
& in(ordered_pair(U_504,sK96(U_501,U_500,U_499,U_504,U_502)),U_501) )
| ~ in(ordered_pair(U_504,U_502),U_499) ) )
| U_499 != relation_composition(U_501,U_500) ) )
| ~ relation(U_499) )
| ~ relation(U_500) )
| ~ relation(U_501) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_496,sK101(U_501,U_500,U_499))],[f_63_8]) ).
cnf(f_63_10,plain,
( in(ordered_pair(U_504,sK96(U_501,U_500,U_499,U_504,U_502)),U_501)
| ~ in(ordered_pair(U_504,U_502),U_499)
| U_499 != relation_composition(U_501,U_500)
| ~ relation(U_499)
| ~ relation(U_500)
| ~ relation(U_501) ),
inference(clausify,[status(thm)],[f_63_9]) ).
cnf(f_63_11,plain,
( in(ordered_pair(sK96(U_501,U_500,U_499,U_504,U_502),U_502),U_500)
| ~ in(ordered_pair(U_504,U_502),U_499)
| U_499 != relation_composition(U_501,U_500)
| ~ relation(U_499)
| ~ relation(U_500)
| ~ relation(U_501) ),
inference(clausify,[status(thm)],[f_63_9]) ).
cnf(f_63_12,plain,
( in(ordered_pair(U_505,U_503),U_499)
| ~ in(ordered_pair(U_492,U_503),U_500)
| ~ in(ordered_pair(U_505,U_492),U_501)
| U_499 != relation_composition(U_501,U_500)
| ~ relation(U_499)
| ~ relation(U_500)
| ~ relation(U_501) ),
inference(clausify,[status(thm)],[f_63_9]) ).
cnf(f_63_13,plain,
( in(ordered_pair(sK99(U_501,U_500,U_499),sK101(U_501,U_500,U_499)),U_501)
| in(ordered_pair(sK97(U_501,U_500,U_499),sK98(U_501,U_500,U_499)),U_499)
| U_499 = relation_composition(U_501,U_500)
| ~ relation(U_499)
| ~ relation(U_500)
| ~ relation(U_501) ),
inference(clausify,[status(thm)],[f_63_9]) ).
cnf(f_63_14,plain,
( in(ordered_pair(sK101(U_501,U_500,U_499),sK100(U_501,U_500,U_499)),U_500)
| in(ordered_pair(sK97(U_501,U_500,U_499),sK98(U_501,U_500,U_499)),U_499)
| U_499 = relation_composition(U_501,U_500)
| ~ relation(U_499)
| ~ relation(U_500)
| ~ relation(U_501) ),
inference(clausify,[status(thm)],[f_63_9]) ).
cnf(f_63_15,plain,
( ~ in(ordered_pair(sK99(U_501,U_500,U_499),sK100(U_501,U_500,U_499)),U_499)
| in(ordered_pair(sK97(U_501,U_500,U_499),sK98(U_501,U_500,U_499)),U_499)
| U_499 = relation_composition(U_501,U_500)
| ~ relation(U_499)
| ~ relation(U_500)
| ~ relation(U_501) ),
inference(clausify,[status(thm)],[f_63_9]) ).
cnf(f_63_16,plain,
( in(ordered_pair(sK99(U_501,U_500,U_499),sK101(U_501,U_500,U_499)),U_501)
| ~ in(ordered_pair(U_495,sK98(U_501,U_500,U_499)),U_500)
| ~ in(ordered_pair(sK97(U_501,U_500,U_499),U_495),U_501)
| U_499 = relation_composition(U_501,U_500)
| ~ relation(U_499)
| ~ relation(U_500)
| ~ relation(U_501) ),
inference(clausify,[status(thm)],[f_63_9]) ).
cnf(f_63_17,plain,
( in(ordered_pair(sK101(U_501,U_500,U_499),sK100(U_501,U_500,U_499)),U_500)
| ~ in(ordered_pair(U_495,sK98(U_501,U_500,U_499)),U_500)
| ~ in(ordered_pair(sK97(U_501,U_500,U_499),U_495),U_501)
| U_499 = relation_composition(U_501,U_500)
| ~ relation(U_499)
| ~ relation(U_500)
| ~ relation(U_501) ),
inference(clausify,[status(thm)],[f_63_9]) ).
cnf(f_63_18,plain,
( ~ in(ordered_pair(sK99(U_501,U_500,U_499),sK100(U_501,U_500,U_499)),U_499)
| ~ in(ordered_pair(U_495,sK98(U_501,U_500,U_499)),U_500)
| ~ in(ordered_pair(sK97(U_501,U_500,U_499),U_495),U_501)
| U_499 = relation_composition(U_501,U_500)
| ~ relation(U_499)
| ~ relation(U_500)
| ~ relation(U_501) ),
inference(clausify,[status(thm)],[f_63_9]) ).
fof(f_64_1,plain,
! [A] :
( ! [B] :
( ( is_transitive_in(A,B)
| ? [C,D,E] :
( ~ in(ordered_pair(C,E),A)
& in(ordered_pair(D,E),A)
& in(ordered_pair(C,D),A)
& in(E,B)
& in(D,B)
& in(C,B) ) )
& ( ! [C,D,E] :
( in(ordered_pair(C,E),A)
| ~ in(ordered_pair(D,E),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(E,B)
| ~ in(D,B)
| ~ in(C,B) )
| ~ is_transitive_in(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d8_relat_2]) ).
fof(f_64_2,plain,
! [U_517] :
( ! [U_516] :
( ( is_transitive_in(U_517,U_516)
| ? [U_515,U_514,U_513] :
( ~ in(ordered_pair(U_515,U_513),U_517)
& in(ordered_pair(U_514,U_513),U_517)
& in(ordered_pair(U_515,U_514),U_517)
& in(U_513,U_516)
& in(U_514,U_516)
& in(U_515,U_516) ) )
& ( ! [U_512,U_511,U_510] :
( in(ordered_pair(U_512,U_510),U_517)
| ~ in(ordered_pair(U_511,U_510),U_517)
| ~ in(ordered_pair(U_512,U_511),U_517)
| ~ in(U_510,U_516)
| ~ in(U_511,U_516)
| ~ in(U_512,U_516) )
| ~ is_transitive_in(U_517,U_516) ) )
| ~ relation(U_517) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
! [U_517] :
( ( ! [U_519] :
( is_transitive_in(U_517,U_519)
| ? [U_515,U_514,U_513] :
( ~ in(ordered_pair(U_515,U_513),U_517)
& in(ordered_pair(U_514,U_513),U_517)
& in(ordered_pair(U_515,U_514),U_517)
& in(U_513,U_519)
& in(U_514,U_519)
& in(U_515,U_519) ) )
& ! [U_518] :
( ! [U_512,U_511,U_510] :
( in(ordered_pair(U_512,U_510),U_517)
| ~ in(ordered_pair(U_511,U_510),U_517)
| ~ in(ordered_pair(U_512,U_511),U_517)
| ~ in(U_510,U_518)
| ~ in(U_511,U_518)
| ~ in(U_512,U_518) )
| ~ is_transitive_in(U_517,U_518) ) )
| ~ relation(U_517) ),
inference(miniscope,[status(thm)],[f_64_2]) ).
fof(f_64_4,plain,
! [U_517] :
( ( ! [U_519] :
( is_transitive_in(U_517,U_519)
| ? [U_514,U_513] :
( ~ in(ordered_pair(sK102(U_517,U_519),U_513),U_517)
& in(ordered_pair(U_514,U_513),U_517)
& in(ordered_pair(sK102(U_517,U_519),U_514),U_517)
& in(U_513,U_519)
& in(U_514,U_519)
& in(sK102(U_517,U_519),U_519) ) )
& ! [U_518] :
( ! [U_512,U_511,U_510] :
( in(ordered_pair(U_512,U_510),U_517)
| ~ in(ordered_pair(U_511,U_510),U_517)
| ~ in(ordered_pair(U_512,U_511),U_517)
| ~ in(U_510,U_518)
| ~ in(U_511,U_518)
| ~ in(U_512,U_518) )
| ~ is_transitive_in(U_517,U_518) ) )
| ~ relation(U_517) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_515,sK102(U_517,U_519))],[f_64_3]) ).
fof(f_64_5,plain,
! [U_517] :
( ( ! [U_519] :
( is_transitive_in(U_517,U_519)
| ? [U_513] :
( ~ in(ordered_pair(sK102(U_517,U_519),U_513),U_517)
& in(ordered_pair(sK103(U_517,U_519),U_513),U_517)
& in(ordered_pair(sK102(U_517,U_519),sK103(U_517,U_519)),U_517)
& in(U_513,U_519)
& in(sK103(U_517,U_519),U_519)
& in(sK102(U_517,U_519),U_519) ) )
& ! [U_518] :
( ! [U_512,U_511,U_510] :
( in(ordered_pair(U_512,U_510),U_517)
| ~ in(ordered_pair(U_511,U_510),U_517)
| ~ in(ordered_pair(U_512,U_511),U_517)
| ~ in(U_510,U_518)
| ~ in(U_511,U_518)
| ~ in(U_512,U_518) )
| ~ is_transitive_in(U_517,U_518) ) )
| ~ relation(U_517) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(U_514,sK103(U_517,U_519))],[f_64_4]) ).
fof(f_64_6,plain,
! [U_517] :
( ( ! [U_519] :
( is_transitive_in(U_517,U_519)
| ( ~ in(ordered_pair(sK102(U_517,U_519),sK104(U_517,U_519)),U_517)
& in(ordered_pair(sK103(U_517,U_519),sK104(U_517,U_519)),U_517)
& in(ordered_pair(sK102(U_517,U_519),sK103(U_517,U_519)),U_517)
& in(sK104(U_517,U_519),U_519)
& in(sK103(U_517,U_519),U_519)
& in(sK102(U_517,U_519),U_519) ) )
& ! [U_518] :
( ! [U_512,U_511,U_510] :
( in(ordered_pair(U_512,U_510),U_517)
| ~ in(ordered_pair(U_511,U_510),U_517)
| ~ in(ordered_pair(U_512,U_511),U_517)
| ~ in(U_510,U_518)
| ~ in(U_511,U_518)
| ~ in(U_512,U_518) )
| ~ is_transitive_in(U_517,U_518) ) )
| ~ relation(U_517) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK104]),skolemize(U_513,sK104(U_517,U_519))],[f_64_5]) ).
cnf(f_64_7,plain,
( in(ordered_pair(U_512,U_510),U_517)
| ~ in(ordered_pair(U_511,U_510),U_517)
| ~ in(ordered_pair(U_512,U_511),U_517)
| ~ in(U_510,U_518)
| ~ in(U_511,U_518)
| ~ in(U_512,U_518)
| ~ is_transitive_in(U_517,U_518)
| ~ relation(U_517) ),
inference(clausify,[status(thm)],[f_64_6]) ).
cnf(f_64_8,plain,
( in(sK102(U_517,U_519),U_519)
| is_transitive_in(U_517,U_519)
| ~ relation(U_517) ),
inference(clausify,[status(thm)],[f_64_6]) ).
cnf(f_64_9,plain,
( in(sK103(U_517,U_519),U_519)
| is_transitive_in(U_517,U_519)
| ~ relation(U_517) ),
inference(clausify,[status(thm)],[f_64_6]) ).
cnf(f_64_10,plain,
( in(sK104(U_517,U_519),U_519)
| is_transitive_in(U_517,U_519)
| ~ relation(U_517) ),
inference(clausify,[status(thm)],[f_64_6]) ).
cnf(f_64_11,plain,
( in(ordered_pair(sK102(U_517,U_519),sK103(U_517,U_519)),U_517)
| is_transitive_in(U_517,U_519)
| ~ relation(U_517) ),
inference(clausify,[status(thm)],[f_64_6]) ).
cnf(f_64_12,plain,
( in(ordered_pair(sK103(U_517,U_519),sK104(U_517,U_519)),U_517)
| is_transitive_in(U_517,U_519)
| ~ relation(U_517) ),
inference(clausify,[status(thm)],[f_64_6]) ).
cnf(f_64_13,plain,
( ~ in(ordered_pair(sK102(U_517,U_519),sK104(U_517,U_519)),U_517)
| is_transitive_in(U_517,U_519)
| ~ relation(U_517) ),
inference(clausify,[status(thm)],[f_64_6]) ).
fof(f_65_1,plain,
! [A,B] :
( ! [C] :
( ( ( C = complements_of_subsets(A,B)
| ? [D] :
( ( ( ~ in(D,C)
& in(subset_complement(A,D),B) )
| ( ~ in(subset_complement(A,D),B)
& in(D,C) ) )
& element(D,powerset(A)) ) )
& ( ! [D] :
( ( ( in(D,C)
| ~ in(subset_complement(A,D),B) )
& ( in(subset_complement(A,D),B)
| ~ in(D,C) ) )
| ~ element(D,powerset(A)) )
| C != complements_of_subsets(A,B) ) )
| ~ element(C,powerset(powerset(A))) )
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[d8_setfam_1]) ).
fof(f_65_2,plain,
! [U_524,U_523] :
( ! [U_522] :
( ( ( U_522 = complements_of_subsets(U_524,U_523)
| ? [U_521] :
( ( ( ~ in(U_521,U_522)
& in(subset_complement(U_524,U_521),U_523) )
| ( ~ in(subset_complement(U_524,U_521),U_523)
& in(U_521,U_522) ) )
& element(U_521,powerset(U_524)) ) )
& ( ! [U_520] :
( ( ( in(U_520,U_522)
| ~ in(subset_complement(U_524,U_520),U_523) )
& ( in(subset_complement(U_524,U_520),U_523)
| ~ in(U_520,U_522) ) )
| ~ element(U_520,powerset(U_524)) )
| U_522 != complements_of_subsets(U_524,U_523) ) )
| ~ element(U_522,powerset(powerset(U_524))) )
| ~ element(U_523,powerset(powerset(U_524))) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
! [U_524,U_523] :
( ! [U_522] :
( ( ( U_522 = complements_of_subsets(U_524,U_523)
| ( ( ( ~ in(sK105(U_524,U_523,U_522),U_522)
& in(subset_complement(U_524,sK105(U_524,U_523,U_522)),U_523) )
| ( ~ in(subset_complement(U_524,sK105(U_524,U_523,U_522)),U_523)
& in(sK105(U_524,U_523,U_522),U_522) ) )
& element(sK105(U_524,U_523,U_522),powerset(U_524)) ) )
& ( ! [U_520] :
( ( ( in(U_520,U_522)
| ~ in(subset_complement(U_524,U_520),U_523) )
& ( in(subset_complement(U_524,U_520),U_523)
| ~ in(U_520,U_522) ) )
| ~ element(U_520,powerset(U_524)) )
| U_522 != complements_of_subsets(U_524,U_523) ) )
| ~ element(U_522,powerset(powerset(U_524))) )
| ~ element(U_523,powerset(powerset(U_524))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK105]),skolemize(U_521,sK105(U_524,U_523,U_522))],[f_65_2]) ).
cnf(f_65_4,plain,
( in(subset_complement(U_524,U_520),U_523)
| ~ in(U_520,U_522)
| ~ element(U_520,powerset(U_524))
| U_522 != complements_of_subsets(U_524,U_523)
| ~ element(U_522,powerset(powerset(U_524)))
| ~ element(U_523,powerset(powerset(U_524))) ),
inference(clausify,[status(thm)],[f_65_3]) ).
cnf(f_65_5,plain,
( in(U_520,U_522)
| ~ in(subset_complement(U_524,U_520),U_523)
| ~ element(U_520,powerset(U_524))
| U_522 != complements_of_subsets(U_524,U_523)
| ~ element(U_522,powerset(powerset(U_524)))
| ~ element(U_523,powerset(powerset(U_524))) ),
inference(clausify,[status(thm)],[f_65_3]) ).
cnf(f_65_6,plain,
( element(sK105(U_524,U_523,U_522),powerset(U_524))
| U_522 = complements_of_subsets(U_524,U_523)
| ~ element(U_522,powerset(powerset(U_524)))
| ~ element(U_523,powerset(powerset(U_524))) ),
inference(clausify,[status(thm)],[f_65_3]) ).
cnf(f_65_7,plain,
( in(subset_complement(U_524,sK105(U_524,U_523,U_522)),U_523)
| in(sK105(U_524,U_523,U_522),U_522)
| U_522 = complements_of_subsets(U_524,U_523)
| ~ element(U_522,powerset(powerset(U_524)))
| ~ element(U_523,powerset(powerset(U_524))) ),
inference(clausify,[status(thm)],[f_65_3]) ).
cnf(f_65_8,plain,
( ~ in(sK105(U_524,U_523,U_522),U_522)
| in(sK105(U_524,U_523,U_522),U_522)
| U_522 = complements_of_subsets(U_524,U_523)
| ~ element(U_522,powerset(powerset(U_524)))
| ~ element(U_523,powerset(powerset(U_524))) ),
inference(clausify,[status(thm)],[f_65_3]) ).
cnf(f_65_9,plain,
( in(subset_complement(U_524,sK105(U_524,U_523,U_522)),U_523)
| ~ in(subset_complement(U_524,sK105(U_524,U_523,U_522)),U_523)
| U_522 = complements_of_subsets(U_524,U_523)
| ~ element(U_522,powerset(powerset(U_524)))
| ~ element(U_523,powerset(powerset(U_524))) ),
inference(clausify,[status(thm)],[f_65_3]) ).
cnf(f_65_10,plain,
( ~ in(sK105(U_524,U_523,U_522),U_522)
| ~ in(subset_complement(U_524,sK105(U_524,U_523,U_522)),U_523)
| U_522 = complements_of_subsets(U_524,U_523)
| ~ element(U_522,powerset(powerset(U_524)))
| ~ element(U_523,powerset(powerset(U_524))) ),
inference(clausify,[status(thm)],[f_65_3]) ).
fof(f_66_1,plain,
! [A,B] :
( ( proper_subset(A,B)
| A = B
| ~ subset(A,B) )
& ( ( A != B
& subset(A,B) )
| ~ proper_subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d8_xboole_0]) ).
fof(f_66_2,plain,
! [U_526,U_525] :
( ( proper_subset(U_526,U_525)
| U_526 = U_525
| ~ subset(U_526,U_525) )
& ( ( U_526 != U_525
& subset(U_526,U_525) )
| ~ proper_subset(U_526,U_525) ) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
( ! [U_530,U_528] :
( proper_subset(U_530,U_528)
| U_530 = U_528
| ~ subset(U_530,U_528) )
& ! [U_529,U_527] :
( ( U_529 != U_527
& subset(U_529,U_527) )
| ~ proper_subset(U_529,U_527) ) ),
inference(miniscope,[status(thm)],[f_66_2]) ).
cnf(f_66_4,plain,
( subset(U_529,U_527)
| ~ proper_subset(U_529,U_527) ),
inference(clausify,[status(thm)],[f_66_3]) ).
cnf(f_66_5,plain,
( U_529 != U_527
| ~ proper_subset(U_529,U_527) ),
inference(clausify,[status(thm)],[f_66_3]) ).
cnf(f_66_6,plain,
( proper_subset(U_530,U_528)
| U_530 = U_528
| ~ subset(U_530,U_528) ),
inference(clausify,[status(thm)],[f_66_3]) ).
fof(f_67_1,plain,
! [A] :
( function_inverse(A) = relation_inverse(A)
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d9_funct_1]) ).
fof(f_67_2,plain,
! [U_531] :
( function_inverse(U_531) = relation_inverse(U_531)
| ~ one_to_one(U_531)
| ~ function(U_531)
| ~ relation(U_531) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
cnf(f_67_3,plain,
( function_inverse(U_531) = relation_inverse(U_531)
| ~ one_to_one(U_531)
| ~ function(U_531)
| ~ relation(U_531) ),
inference(clausify,[status(thm)],[f_67_2]) ).
fof(f_68_1,plain,
! [A] :
( ( ( reflexive(A)
| ~ is_reflexive_in(A,relation_field(A)) )
& ( is_reflexive_in(A,relation_field(A))
| ~ reflexive(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d9_relat_2]) ).
fof(f_68_2,plain,
! [U_532] :
( ( ( reflexive(U_532)
| ~ is_reflexive_in(U_532,relation_field(U_532)) )
& ( is_reflexive_in(U_532,relation_field(U_532))
| ~ reflexive(U_532) ) )
| ~ relation(U_532) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
cnf(f_68_3,plain,
( is_reflexive_in(U_532,relation_field(U_532))
| ~ reflexive(U_532)
| ~ relation(U_532) ),
inference(clausify,[status(thm)],[f_68_2]) ).
cnf(f_68_4,plain,
( reflexive(U_532)
| ~ is_reflexive_in(U_532,relation_field(U_532))
| ~ relation(U_532) ),
inference(clausify,[status(thm)],[f_68_2]) ).
fof(f_69_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k10_relat_1]) ).
cnf(f_69_2,plain,
$true,
inference(clausify,[status(thm)],[f_69_1]) ).
fof(f_70_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_enumset1]) ).
cnf(f_70_2,plain,
$true,
inference(clausify,[status(thm)],[f_70_1]) ).
fof(f_71_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_funct_1]) ).
cnf(f_71_2,plain,
$true,
inference(clausify,[status(thm)],[f_71_1]) ).
fof(f_72_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_ordinal1]) ).
cnf(f_72_2,plain,
$true,
inference(clausify,[status(thm)],[f_72_1]) ).
fof(f_73_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
cnf(f_73_2,plain,
$true,
inference(clausify,[status(thm)],[f_73_1]) ).
fof(f_74_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_setfam_1]) ).
cnf(f_74_2,plain,
$true,
inference(clausify,[status(thm)],[f_74_1]) ).
fof(f_75_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
cnf(f_75_2,plain,
$true,
inference(clausify,[status(thm)],[f_75_1]) ).
fof(f_76_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_wellord1]) ).
cnf(f_76_2,plain,
$true,
inference(clausify,[status(thm)],[f_76_1]) ).
fof(f_77_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_77_2,plain,
$true,
inference(clausify,[status(thm)],[f_77_1]) ).
fof(f_78_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_78_2,plain,
$true,
inference(clausify,[status(thm)],[f_78_1]) ).
fof(f_79_1,plain,
! [A] :
( ( function(function_inverse(A))
& relation(function_inverse(A)) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_funct_1]) ).
fof(f_79_2,plain,
! [U_533] :
( ( function(function_inverse(U_533))
& relation(function_inverse(U_533)) )
| ~ function(U_533)
| ~ relation(U_533) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
cnf(f_79_3,plain,
( relation(function_inverse(U_533))
| ~ function(U_533)
| ~ relation(U_533) ),
inference(clausify,[status(thm)],[f_79_2]) ).
cnf(f_79_4,plain,
( function(function_inverse(U_533))
| ~ function(U_533)
| ~ relation(U_533) ),
inference(clausify,[status(thm)],[f_79_2]) ).
fof(f_80_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_relat_1]) ).
cnf(f_80_2,plain,
$true,
inference(clausify,[status(thm)],[f_80_1]) ).
fof(f_81_1,plain,
! [A] : element(cast_to_subset(A),powerset(A)),
inference(fof_nnf,[status(thm)],[dt_k2_subset_1]) ).
fof(f_81_2,plain,
! [U_534] : element(cast_to_subset(U_534),powerset(U_534)),
inference(variable_rename,[status(thm)],[f_81_1]) ).
cnf(f_81_3,plain,
element(cast_to_subset(U_534),powerset(U_534)),
inference(clausify,[status(thm)],[f_81_2]) ).
fof(f_82_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
cnf(f_82_2,plain,
$true,
inference(clausify,[status(thm)],[f_82_1]) ).
fof(f_83_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
cnf(f_83_2,plain,
$true,
inference(clausify,[status(thm)],[f_83_1]) ).
fof(f_84_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
cnf(f_84_2,plain,
$true,
inference(clausify,[status(thm)],[f_84_1]) ).
fof(f_85_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_relat_1]) ).
cnf(f_85_2,plain,
$true,
inference(clausify,[status(thm)],[f_85_1]) ).
fof(f_86_1,plain,
! [A,B] :
( element(subset_complement(A,B),powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[dt_k3_subset_1]) ).
fof(f_86_2,plain,
! [U_536,U_535] :
( element(subset_complement(U_536,U_535),powerset(U_536))
| ~ element(U_535,powerset(U_536)) ),
inference(variable_rename,[status(thm)],[f_86_1]) ).
cnf(f_86_3,plain,
( element(subset_complement(U_536,U_535),powerset(U_536))
| ~ element(U_535,powerset(U_536)) ),
inference(clausify,[status(thm)],[f_86_2]) ).
fof(f_87_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_tarski]) ).
cnf(f_87_2,plain,
$true,
inference(clausify,[status(thm)],[f_87_1]) ).
fof(f_88_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
cnf(f_88_2,plain,
$true,
inference(clausify,[status(thm)],[f_88_1]) ).
fof(f_89_1,plain,
! [A] :
( relation(relation_inverse(A))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k4_relat_1]) ).
fof(f_89_2,plain,
! [U_537] :
( relation(relation_inverse(U_537))
| ~ relation(U_537) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
cnf(f_89_3,plain,
( relation(relation_inverse(U_537))
| ~ relation(U_537) ),
inference(clausify,[status(thm)],[f_89_2]) ).
fof(f_90_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
cnf(f_90_2,plain,
$true,
inference(clausify,[status(thm)],[f_90_1]) ).
fof(f_91_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
cnf(f_91_2,plain,
$true,
inference(clausify,[status(thm)],[f_91_1]) ).
fof(f_92_1,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_relat_1]) ).
fof(f_92_2,plain,
! [U_539,U_538] :
( relation(relation_composition(U_539,U_538))
| ~ relation(U_538)
| ~ relation(U_539) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
cnf(f_92_3,plain,
( relation(relation_composition(U_539,U_538))
| ~ relation(U_538)
| ~ relation(U_539) ),
inference(clausify,[status(thm)],[f_92_2]) ).
fof(f_93_1,plain,
! [A,B] :
( element(union_of_subsets(A,B),powerset(A))
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[dt_k5_setfam_1]) ).
fof(f_93_2,plain,
! [U_541,U_540] :
( element(union_of_subsets(U_541,U_540),powerset(U_541))
| ~ element(U_540,powerset(powerset(U_541))) ),
inference(variable_rename,[status(thm)],[f_93_1]) ).
cnf(f_93_3,plain,
( element(union_of_subsets(U_541,U_540),powerset(U_541))
| ~ element(U_540,powerset(powerset(U_541))) ),
inference(clausify,[status(thm)],[f_93_2]) ).
fof(f_94_1,plain,
! [A] : relation(identity_relation(A)),
inference(fof_nnf,[status(thm)],[dt_k6_relat_1]) ).
fof(f_94_2,plain,
! [U_542] : relation(identity_relation(U_542)),
inference(variable_rename,[status(thm)],[f_94_1]) ).
cnf(f_94_3,plain,
relation(identity_relation(U_542)),
inference(clausify,[status(thm)],[f_94_2]) ).
fof(f_95_1,plain,
! [A,B] :
( element(meet_of_subsets(A,B),powerset(A))
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[dt_k6_setfam_1]) ).
fof(f_95_2,plain,
! [U_544,U_543] :
( element(meet_of_subsets(U_544,U_543),powerset(U_544))
| ~ element(U_543,powerset(powerset(U_544))) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
cnf(f_95_3,plain,
( element(meet_of_subsets(U_544,U_543),powerset(U_544))
| ~ element(U_543,powerset(powerset(U_544))) ),
inference(clausify,[status(thm)],[f_95_2]) ).
fof(f_96_1,plain,
! [A,B,C] :
( element(subset_difference(A,B,C),powerset(A))
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[dt_k6_subset_1]) ).
fof(f_96_2,plain,
! [U_547,U_546,U_545] :
( element(subset_difference(U_547,U_546,U_545),powerset(U_547))
| ~ element(U_545,powerset(U_547))
| ~ element(U_546,powerset(U_547)) ),
inference(variable_rename,[status(thm)],[f_96_1]) ).
cnf(f_96_3,plain,
( element(subset_difference(U_547,U_546,U_545),powerset(U_547))
| ~ element(U_545,powerset(U_547))
| ~ element(U_546,powerset(U_547)) ),
inference(clausify,[status(thm)],[f_96_2]) ).
fof(f_97_1,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k7_relat_1]) ).
fof(f_97_2,plain,
! [U_549,U_548] :
( relation(relation_dom_restriction(U_549,U_548))
| ~ relation(U_549) ),
inference(variable_rename,[status(thm)],[f_97_1]) ).
fof(f_97_3,plain,
! [U_549] :
( ! [U_548] : relation(relation_dom_restriction(U_549,U_548))
| ~ relation(U_549) ),
inference(miniscope,[status(thm)],[f_97_2]) ).
cnf(f_97_4,plain,
( relation(relation_dom_restriction(U_549,U_548))
| ~ relation(U_549) ),
inference(clausify,[status(thm)],[f_97_3]) ).
fof(f_98_1,plain,
! [A,B] :
( element(complements_of_subsets(A,B),powerset(powerset(A)))
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[dt_k7_setfam_1]) ).
fof(f_98_2,plain,
! [U_551,U_550] :
( element(complements_of_subsets(U_551,U_550),powerset(powerset(U_551)))
| ~ element(U_550,powerset(powerset(U_551))) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
cnf(f_98_3,plain,
( element(complements_of_subsets(U_551,U_550),powerset(powerset(U_551)))
| ~ element(U_550,powerset(powerset(U_551))) ),
inference(clausify,[status(thm)],[f_98_2]) ).
fof(f_99_1,plain,
! [A,B] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[dt_k8_relat_1]) ).
fof(f_99_2,plain,
! [U_553,U_552] :
( relation(relation_rng_restriction(U_553,U_552))
| ~ relation(U_552) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
cnf(f_99_3,plain,
( relation(relation_rng_restriction(U_553,U_552))
| ~ relation(U_552) ),
inference(clausify,[status(thm)],[f_99_2]) ).
fof(f_100_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k9_relat_1]) ).
cnf(f_100_2,plain,
$true,
inference(clausify,[status(thm)],[f_100_1]) ).
fof(f_101_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_101_2,plain,
$true,
inference(clausify,[status(thm)],[f_101_1]) ).
fof(f_102_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_102_2,plain,
! [U_555] :
? [U_554] : element(U_554,U_555),
inference(variable_rename,[status(thm)],[f_102_1]) ).
fof(f_102_3,plain,
! [U_555] : element(sK106(U_555),U_555),
inference(skolemize,[status(esa),new_symbols(skolem,[sK106]),skolemize(U_554,sK106(U_555))],[f_102_2]) ).
cnf(f_102_4,plain,
element(sK106(U_555),U_555),
inference(clausify,[status(thm)],[f_102_3]) ).
fof(f_103_1,plain,
! [A,B] :
( ( relation(relation_composition(B,A))
& empty(relation_composition(B,A)) )
| ~ relation(B)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc10_relat_1]) ).
fof(f_103_2,plain,
! [U_557,U_556] :
( ( relation(relation_composition(U_556,U_557))
& empty(relation_composition(U_556,U_557)) )
| ~ relation(U_556)
| ~ empty(U_557) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
cnf(f_103_3,plain,
( empty(relation_composition(U_556,U_557))
| ~ relation(U_556)
| ~ empty(U_557) ),
inference(clausify,[status(thm)],[f_103_2]) ).
cnf(f_103_4,plain,
( relation(relation_composition(U_556,U_557))
| ~ relation(U_556)
| ~ empty(U_557) ),
inference(clausify,[status(thm)],[f_103_2]) ).
fof(f_104_1,plain,
! [A] :
( ( relation(relation_inverse(A))
& empty(relation_inverse(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc11_relat_1]) ).
fof(f_104_2,plain,
! [U_558] :
( ( relation(relation_inverse(U_558))
& empty(relation_inverse(U_558)) )
| ~ empty(U_558) ),
inference(variable_rename,[status(thm)],[f_104_1]) ).
cnf(f_104_3,plain,
( empty(relation_inverse(U_558))
| ~ empty(U_558) ),
inference(clausify,[status(thm)],[f_104_2]) ).
cnf(f_104_4,plain,
( relation(relation_inverse(U_558))
| ~ empty(U_558) ),
inference(clausify,[status(thm)],[f_104_2]) ).
fof(f_105_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
cnf(f_105_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_105_1]) ).
cnf(f_105_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_105_1]) ).
cnf(f_105_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_105_1]) ).
fof(f_106_1,plain,
! [A,B] :
( ( relation_empty_yielding(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) )
| ~ relation_empty_yielding(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc13_relat_1]) ).
fof(f_106_2,plain,
! [U_560,U_559] :
( ( relation_empty_yielding(relation_dom_restriction(U_560,U_559))
& relation(relation_dom_restriction(U_560,U_559)) )
| ~ relation_empty_yielding(U_560)
| ~ relation(U_560) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
fof(f_106_3,plain,
! [U_560] :
( ( ! [U_562] : relation_empty_yielding(relation_dom_restriction(U_560,U_562))
& ! [U_561] : relation(relation_dom_restriction(U_560,U_561)) )
| ~ relation_empty_yielding(U_560)
| ~ relation(U_560) ),
inference(miniscope,[status(thm)],[f_106_2]) ).
cnf(f_106_4,plain,
( relation(relation_dom_restriction(U_560,U_561))
| ~ relation_empty_yielding(U_560)
| ~ relation(U_560) ),
inference(clausify,[status(thm)],[f_106_3]) ).
cnf(f_106_5,plain,
( relation_empty_yielding(relation_dom_restriction(U_560,U_562))
| ~ relation_empty_yielding(U_560)
| ~ relation(U_560) ),
inference(clausify,[status(thm)],[f_106_3]) ).
fof(f_107_1,plain,
! [A,B] :
( ( function(relation_composition(A,B))
& relation(relation_composition(A,B)) )
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc1_funct_1]) ).
fof(f_107_2,plain,
! [U_564,U_563] :
( ( function(relation_composition(U_564,U_563))
& relation(relation_composition(U_564,U_563)) )
| ~ function(U_563)
| ~ relation(U_563)
| ~ function(U_564)
| ~ relation(U_564) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
cnf(f_107_3,plain,
( relation(relation_composition(U_564,U_563))
| ~ function(U_563)
| ~ relation(U_563)
| ~ function(U_564)
| ~ relation(U_564) ),
inference(clausify,[status(thm)],[f_107_2]) ).
cnf(f_107_4,plain,
( function(relation_composition(U_564,U_563))
| ~ function(U_563)
| ~ relation(U_563)
| ~ function(U_564)
| ~ relation(U_564) ),
inference(clausify,[status(thm)],[f_107_2]) ).
fof(f_108_1,plain,
! [A] : ~ empty(succ(A)),
inference(fof_nnf,[status(thm)],[fc1_ordinal1]) ).
fof(f_108_2,plain,
! [U_565] : ~ empty(succ(U_565)),
inference(variable_rename,[status(thm)],[f_108_1]) ).
cnf(f_108_3,plain,
~ empty(succ(U_565)),
inference(clausify,[status(thm)],[f_108_2]) ).
fof(f_109_1,plain,
! [A,B] :
( relation(set_intersection2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc1_relat_1]) ).
fof(f_109_2,plain,
! [U_567,U_566] :
( relation(set_intersection2(U_567,U_566))
| ~ relation(U_566)
| ~ relation(U_567) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
cnf(f_109_3,plain,
( relation(set_intersection2(U_567,U_566))
| ~ relation(U_566)
| ~ relation(U_567) ),
inference(clausify,[status(thm)],[f_109_2]) ).
fof(f_110_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_110_2,plain,
! [U_568] : ~ empty(powerset(U_568)),
inference(variable_rename,[status(thm)],[f_110_1]) ).
cnf(f_110_3,plain,
~ empty(powerset(U_568)),
inference(clausify,[status(thm)],[f_110_2]) ).
fof(f_111_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_111_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_111_1]) ).
fof(f_112_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_112_2,plain,
! [U_570,U_569] : ~ empty(ordered_pair(U_570,U_569)),
inference(variable_rename,[status(thm)],[f_112_1]) ).
cnf(f_112_3,plain,
~ empty(ordered_pair(U_570,U_569)),
inference(clausify,[status(thm)],[f_112_2]) ).
fof(f_113_1,plain,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
inference(fof_nnf,[status(thm)],[fc2_funct_1]) ).
fof(f_113_2,plain,
! [U_571] :
( function(identity_relation(U_571))
& relation(identity_relation(U_571)) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
fof(f_113_3,plain,
( ! [U_573] : function(identity_relation(U_573))
& ! [U_572] : relation(identity_relation(U_572)) ),
inference(miniscope,[status(thm)],[f_113_2]) ).
cnf(f_113_4,plain,
relation(identity_relation(U_572)),
inference(clausify,[status(thm)],[f_113_3]) ).
cnf(f_113_5,plain,
function(identity_relation(U_573)),
inference(clausify,[status(thm)],[f_113_3]) ).
fof(f_114_1,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
inference(fof_nnf,[status(thm)],[fc2_ordinal1]) ).
cnf(f_114_2,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_114_1]) ).
cnf(f_114_3,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_114_1]) ).
cnf(f_114_4,plain,
function(empty_set),
inference(clausify,[status(thm)],[f_114_1]) ).
cnf(f_114_5,plain,
one_to_one(empty_set),
inference(clausify,[status(thm)],[f_114_1]) ).
cnf(f_114_6,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_114_1]) ).
cnf(f_114_7,plain,
epsilon_transitive(empty_set),
inference(clausify,[status(thm)],[f_114_1]) ).
cnf(f_114_8,plain,
epsilon_connected(empty_set),
inference(clausify,[status(thm)],[f_114_1]) ).
cnf(f_114_9,plain,
ordinal(empty_set),
inference(clausify,[status(thm)],[f_114_1]) ).
fof(f_115_1,plain,
! [A,B] :
( relation(set_union2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc2_relat_1]) ).
fof(f_115_2,plain,
! [U_575,U_574] :
( relation(set_union2(U_575,U_574))
| ~ relation(U_574)
| ~ relation(U_575) ),
inference(variable_rename,[status(thm)],[f_115_1]) ).
cnf(f_115_3,plain,
( relation(set_union2(U_575,U_574))
| ~ relation(U_574)
| ~ relation(U_575) ),
inference(clausify,[status(thm)],[f_115_2]) ).
fof(f_116_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_116_2,plain,
! [U_576] : ~ empty(singleton(U_576)),
inference(variable_rename,[status(thm)],[f_116_1]) ).
cnf(f_116_3,plain,
~ empty(singleton(U_576)),
inference(clausify,[status(thm)],[f_116_2]) ).
fof(f_117_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_117_2,plain,
! [U_578,U_577] :
( ~ empty(set_union2(U_578,U_577))
| empty(U_578) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
fof(f_117_3,plain,
! [U_578] :
( ! [U_577] : ~ empty(set_union2(U_578,U_577))
| empty(U_578) ),
inference(miniscope,[status(thm)],[f_117_2]) ).
cnf(f_117_4,plain,
( ~ empty(set_union2(U_578,U_577))
| empty(U_578) ),
inference(clausify,[status(thm)],[f_117_3]) ).
fof(f_118_1,plain,
! [A] :
( ( function(relation_inverse(A))
& relation(relation_inverse(A)) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc3_funct_1]) ).
fof(f_118_2,plain,
! [U_579] :
( ( function(relation_inverse(U_579))
& relation(relation_inverse(U_579)) )
| ~ one_to_one(U_579)
| ~ function(U_579)
| ~ relation(U_579) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
cnf(f_118_3,plain,
( relation(relation_inverse(U_579))
| ~ one_to_one(U_579)
| ~ function(U_579)
| ~ relation(U_579) ),
inference(clausify,[status(thm)],[f_118_2]) ).
cnf(f_118_4,plain,
( function(relation_inverse(U_579))
| ~ one_to_one(U_579)
| ~ function(U_579)
| ~ relation(U_579) ),
inference(clausify,[status(thm)],[f_118_2]) ).
fof(f_119_1,plain,
! [A] :
( ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[fc3_ordinal1]) ).
fof(f_119_2,plain,
! [U_580] :
( ( ordinal(succ(U_580))
& epsilon_connected(succ(U_580))
& epsilon_transitive(succ(U_580))
& ~ empty(succ(U_580)) )
| ~ ordinal(U_580) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
cnf(f_119_3,plain,
( ~ empty(succ(U_580))
| ~ ordinal(U_580) ),
inference(clausify,[status(thm)],[f_119_2]) ).
cnf(f_119_4,plain,
( epsilon_transitive(succ(U_580))
| ~ ordinal(U_580) ),
inference(clausify,[status(thm)],[f_119_2]) ).
cnf(f_119_5,plain,
( epsilon_connected(succ(U_580))
| ~ ordinal(U_580) ),
inference(clausify,[status(thm)],[f_119_2]) ).
cnf(f_119_6,plain,
( ordinal(succ(U_580))
| ~ ordinal(U_580) ),
inference(clausify,[status(thm)],[f_119_2]) ).
fof(f_120_1,plain,
! [A,B] :
( relation(set_difference(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc3_relat_1]) ).
fof(f_120_2,plain,
! [U_582,U_581] :
( relation(set_difference(U_582,U_581))
| ~ relation(U_581)
| ~ relation(U_582) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
cnf(f_120_3,plain,
( relation(set_difference(U_582,U_581))
| ~ relation(U_581)
| ~ relation(U_582) ),
inference(clausify,[status(thm)],[f_120_2]) ).
fof(f_121_1,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_121_2,plain,
! [U_584,U_583] : ~ empty(unordered_pair(U_584,U_583)),
inference(variable_rename,[status(thm)],[f_121_1]) ).
cnf(f_121_3,plain,
~ empty(unordered_pair(U_584,U_583)),
inference(clausify,[status(thm)],[f_121_2]) ).
fof(f_122_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_122_2,plain,
! [U_586,U_585] :
( ~ empty(set_union2(U_585,U_586))
| empty(U_586) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
fof(f_122_3,plain,
! [U_586] :
( ! [U_585] : ~ empty(set_union2(U_585,U_586))
| empty(U_586) ),
inference(miniscope,[status(thm)],[f_122_2]) ).
cnf(f_122_4,plain,
( ~ empty(set_union2(U_585,U_586))
| empty(U_586) ),
inference(clausify,[status(thm)],[f_122_3]) ).
fof(f_123_1,plain,
! [A,B] :
( ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc4_funct_1]) ).
fof(f_123_2,plain,
! [U_588,U_587] :
( ( function(relation_dom_restriction(U_588,U_587))
& relation(relation_dom_restriction(U_588,U_587)) )
| ~ function(U_588)
| ~ relation(U_588) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
fof(f_123_3,plain,
! [U_588] :
( ( ! [U_590] : function(relation_dom_restriction(U_588,U_590))
& ! [U_589] : relation(relation_dom_restriction(U_588,U_589)) )
| ~ function(U_588)
| ~ relation(U_588) ),
inference(miniscope,[status(thm)],[f_123_2]) ).
cnf(f_123_4,plain,
( relation(relation_dom_restriction(U_588,U_589))
| ~ function(U_588)
| ~ relation(U_588) ),
inference(clausify,[status(thm)],[f_123_3]) ).
cnf(f_123_5,plain,
( function(relation_dom_restriction(U_588,U_590))
| ~ function(U_588)
| ~ relation(U_588) ),
inference(clausify,[status(thm)],[f_123_3]) ).
fof(f_124_1,plain,
! [A] :
( ( ordinal(union(A))
& epsilon_connected(union(A))
& epsilon_transitive(union(A)) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[fc4_ordinal1]) ).
fof(f_124_2,plain,
! [U_591] :
( ( ordinal(union(U_591))
& epsilon_connected(union(U_591))
& epsilon_transitive(union(U_591)) )
| ~ ordinal(U_591) ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
cnf(f_124_3,plain,
( epsilon_transitive(union(U_591))
| ~ ordinal(U_591) ),
inference(clausify,[status(thm)],[f_124_2]) ).
cnf(f_124_4,plain,
( epsilon_connected(union(U_591))
| ~ ordinal(U_591) ),
inference(clausify,[status(thm)],[f_124_2]) ).
cnf(f_124_5,plain,
( ordinal(union(U_591))
| ~ ordinal(U_591) ),
inference(clausify,[status(thm)],[f_124_2]) ).
fof(f_125_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_125_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_125_1]) ).
cnf(f_125_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_125_1]) ).
fof(f_126_1,plain,
! [A,B] :
( ~ empty(cartesian_product2(A,B))
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc4_subset_1]) ).
fof(f_126_2,plain,
! [U_593,U_592] :
( ~ empty(cartesian_product2(U_593,U_592))
| empty(U_592)
| empty(U_593) ),
inference(variable_rename,[status(thm)],[f_126_1]) ).
cnf(f_126_3,plain,
( ~ empty(cartesian_product2(U_593,U_592))
| empty(U_592)
| empty(U_593) ),
inference(clausify,[status(thm)],[f_126_2]) ).
fof(f_127_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_127_2,plain,
! [U_594] :
( ~ empty(relation_dom(U_594))
| ~ relation(U_594)
| empty(U_594) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
cnf(f_127_3,plain,
( ~ empty(relation_dom(U_594))
| ~ relation(U_594)
| empty(U_594) ),
inference(clausify,[status(thm)],[f_127_2]) ).
fof(f_128_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_128_2,plain,
! [U_595] :
( ~ empty(relation_rng(U_595))
| ~ relation(U_595)
| empty(U_595) ),
inference(variable_rename,[status(thm)],[f_128_1]) ).
cnf(f_128_3,plain,
( ~ empty(relation_rng(U_595))
| ~ relation(U_595)
| empty(U_595) ),
inference(clausify,[status(thm)],[f_128_2]) ).
fof(f_129_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_129_2,plain,
! [U_596] :
( ( relation(relation_dom(U_596))
& empty(relation_dom(U_596)) )
| ~ empty(U_596) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
cnf(f_129_3,plain,
( empty(relation_dom(U_596))
| ~ empty(U_596) ),
inference(clausify,[status(thm)],[f_129_2]) ).
cnf(f_129_4,plain,
( relation(relation_dom(U_596))
| ~ empty(U_596) ),
inference(clausify,[status(thm)],[f_129_2]) ).
fof(f_130_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_130_2,plain,
! [U_597] :
( ( relation(relation_rng(U_597))
& empty(relation_rng(U_597)) )
| ~ empty(U_597) ),
inference(variable_rename,[status(thm)],[f_130_1]) ).
cnf(f_130_3,plain,
( empty(relation_rng(U_597))
| ~ empty(U_597) ),
inference(clausify,[status(thm)],[f_130_2]) ).
cnf(f_130_4,plain,
( relation(relation_rng(U_597))
| ~ empty(U_597) ),
inference(clausify,[status(thm)],[f_130_2]) ).
fof(f_131_1,plain,
! [A,B] :
( ( relation(relation_composition(A,B))
& empty(relation_composition(A,B)) )
| ~ relation(B)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc9_relat_1]) ).
fof(f_131_2,plain,
! [U_599,U_598] :
( ( relation(relation_composition(U_599,U_598))
& empty(relation_composition(U_599,U_598)) )
| ~ relation(U_598)
| ~ empty(U_599) ),
inference(variable_rename,[status(thm)],[f_131_1]) ).
cnf(f_131_3,plain,
( empty(relation_composition(U_599,U_598))
| ~ relation(U_598)
| ~ empty(U_599) ),
inference(clausify,[status(thm)],[f_131_2]) ).
cnf(f_131_4,plain,
( relation(relation_composition(U_599,U_598))
| ~ relation(U_598)
| ~ empty(U_599) ),
inference(clausify,[status(thm)],[f_131_2]) ).
fof(f_132_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_132_2,plain,
! [U_601,U_600] : set_union2(U_601,U_601) = U_601,
inference(variable_rename,[status(thm)],[f_132_1]) ).
fof(f_132_3,plain,
! [U_601] : set_union2(U_601,U_601) = U_601,
inference(miniscope,[status(thm)],[f_132_2]) ).
cnf(f_132_4,plain,
set_union2(U_601,U_601) = U_601,
inference(clausify,[status(thm)],[f_132_3]) ).
fof(f_133_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_133_2,plain,
! [U_603,U_602] : set_intersection2(U_603,U_603) = U_603,
inference(variable_rename,[status(thm)],[f_133_1]) ).
fof(f_133_3,plain,
! [U_603] : set_intersection2(U_603,U_603) = U_603,
inference(miniscope,[status(thm)],[f_133_2]) ).
cnf(f_133_4,plain,
set_intersection2(U_603,U_603) = U_603,
inference(clausify,[status(thm)],[f_133_3]) ).
fof(f_134_1,plain,
! [A,B] :
( subset_complement(A,subset_complement(A,B)) = B
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1]) ).
fof(f_134_2,plain,
! [U_605,U_604] :
( subset_complement(U_605,subset_complement(U_605,U_604)) = U_604
| ~ element(U_604,powerset(U_605)) ),
inference(variable_rename,[status(thm)],[f_134_1]) ).
cnf(f_134_3,plain,
( subset_complement(U_605,subset_complement(U_605,U_604)) = U_604
| ~ element(U_604,powerset(U_605)) ),
inference(clausify,[status(thm)],[f_134_2]) ).
fof(f_135_1,plain,
! [A] :
( relation_inverse(relation_inverse(A)) = A
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[involutiveness_k4_relat_1]) ).
fof(f_135_2,plain,
! [U_606] :
( relation_inverse(relation_inverse(U_606)) = U_606
| ~ relation(U_606) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
cnf(f_135_3,plain,
( relation_inverse(relation_inverse(U_606)) = U_606
| ~ relation(U_606) ),
inference(clausify,[status(thm)],[f_135_2]) ).
fof(f_136_1,plain,
! [A,B] :
( complements_of_subsets(A,complements_of_subsets(A,B)) = B
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[involutiveness_k7_setfam_1]) ).
fof(f_136_2,plain,
! [U_608,U_607] :
( complements_of_subsets(U_608,complements_of_subsets(U_608,U_607)) = U_607
| ~ element(U_607,powerset(powerset(U_608))) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
cnf(f_136_3,plain,
( complements_of_subsets(U_608,complements_of_subsets(U_608,U_607)) = U_607
| ~ element(U_607,powerset(powerset(U_608))) ),
inference(clausify,[status(thm)],[f_136_2]) ).
fof(f_137_1,plain,
! [A,B] : ~ proper_subset(A,A),
inference(fof_nnf,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(f_137_2,plain,
! [U_610,U_609] : ~ proper_subset(U_610,U_610),
inference(variable_rename,[status(thm)],[f_137_1]) ).
fof(f_137_3,plain,
! [U_610] : ~ proper_subset(U_610,U_610),
inference(miniscope,[status(thm)],[f_137_2]) ).
cnf(f_137_4,plain,
~ proper_subset(U_610,U_610),
inference(clausify,[status(thm)],[f_137_3]) ).
fof(f_138_1,plain,
! [A] :
( ( ( reflexive(A)
| ? [B] :
( ~ in(ordered_pair(B,B),A)
& in(B,relation_field(A)) ) )
& ( ! [B] :
( in(ordered_pair(B,B),A)
| ~ in(B,relation_field(A)) )
| ~ reflexive(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[l1_wellord1]) ).
fof(f_138_2,plain,
! [U_613] :
( ( ( reflexive(U_613)
| ? [U_612] :
( ~ in(ordered_pair(U_612,U_612),U_613)
& in(U_612,relation_field(U_613)) ) )
& ( ! [U_611] :
( in(ordered_pair(U_611,U_611),U_613)
| ~ in(U_611,relation_field(U_613)) )
| ~ reflexive(U_613) ) )
| ~ relation(U_613) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
fof(f_138_3,plain,
! [U_613] :
( ( ( reflexive(U_613)
| ( ~ in(ordered_pair(sK107(U_613),sK107(U_613)),U_613)
& in(sK107(U_613),relation_field(U_613)) ) )
& ( ! [U_611] :
( in(ordered_pair(U_611,U_611),U_613)
| ~ in(U_611,relation_field(U_613)) )
| ~ reflexive(U_613) ) )
| ~ relation(U_613) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(U_612,sK107(U_613))],[f_138_2]) ).
cnf(f_138_4,plain,
( in(ordered_pair(U_611,U_611),U_613)
| ~ in(U_611,relation_field(U_613))
| ~ reflexive(U_613)
| ~ relation(U_613) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_5,plain,
( in(sK107(U_613),relation_field(U_613))
| reflexive(U_613)
| ~ relation(U_613) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_6,plain,
( ~ in(ordered_pair(sK107(U_613),sK107(U_613)),U_613)
| reflexive(U_613)
| ~ relation(U_613) ),
inference(clausify,[status(thm)],[f_138_3]) ).
fof(f_139_1,plain,
! [A] : singleton(A) != empty_set,
inference(fof_nnf,[status(thm)],[l1_zfmisc_1]) ).
fof(f_139_2,plain,
! [U_614] : singleton(U_614) != empty_set,
inference(variable_rename,[status(thm)],[f_139_1]) ).
cnf(f_139_3,plain,
singleton(U_614) != empty_set,
inference(clausify,[status(thm)],[f_139_2]) ).
fof(f_140_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l23_zfmisc_1]) ).
fof(f_140_2,plain,
! [U_616,U_615] :
( set_union2(singleton(U_616),U_615) = U_615
| ~ in(U_616,U_615) ),
inference(variable_rename,[status(thm)],[f_140_1]) ).
cnf(f_140_3,plain,
( set_union2(singleton(U_616),U_615) = U_615
| ~ in(U_616,U_615) ),
inference(clausify,[status(thm)],[f_140_2]) ).
fof(f_141_1,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(fof_nnf,[status(thm)],[l25_zfmisc_1]) ).
fof(f_141_2,plain,
! [U_618,U_617] :
( ~ in(U_618,U_617)
| ~ disjoint(singleton(U_618),U_617) ),
inference(variable_rename,[status(thm)],[f_141_1]) ).
cnf(f_141_3,plain,
( ~ in(U_618,U_617)
| ~ disjoint(singleton(U_618),U_617) ),
inference(clausify,[status(thm)],[f_141_2]) ).
fof(f_142_1,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(fof_nnf,[status(thm)],[l28_zfmisc_1]) ).
fof(f_142_2,plain,
! [U_620,U_619] :
( disjoint(singleton(U_620),U_619)
| in(U_620,U_619) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
cnf(f_142_3,plain,
( disjoint(singleton(U_620),U_619)
| in(U_620,U_619) ),
inference(clausify,[status(thm)],[f_142_2]) ).
fof(f_143_1,plain,
! [A] :
( ( ( transitive(A)
| ? [B,C,D] :
( ~ in(ordered_pair(B,D),A)
& in(ordered_pair(C,D),A)
& in(ordered_pair(B,C),A) ) )
& ( ! [B,C,D] :
( in(ordered_pair(B,D),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(ordered_pair(B,C),A) )
| ~ transitive(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[l2_wellord1]) ).
fof(f_143_2,plain,
! [U_627] :
( ( ( transitive(U_627)
| ? [U_626,U_625,U_624] :
( ~ in(ordered_pair(U_626,U_624),U_627)
& in(ordered_pair(U_625,U_624),U_627)
& in(ordered_pair(U_626,U_625),U_627) ) )
& ( ! [U_623,U_622,U_621] :
( in(ordered_pair(U_623,U_621),U_627)
| ~ in(ordered_pair(U_622,U_621),U_627)
| ~ in(ordered_pair(U_623,U_622),U_627) )
| ~ transitive(U_627) ) )
| ~ relation(U_627) ),
inference(variable_rename,[status(thm)],[f_143_1]) ).
fof(f_143_3,plain,
! [U_627] :
( ( ( transitive(U_627)
| ? [U_625,U_624] :
( ~ in(ordered_pair(sK108(U_627),U_624),U_627)
& in(ordered_pair(U_625,U_624),U_627)
& in(ordered_pair(sK108(U_627),U_625),U_627) ) )
& ( ! [U_623,U_622,U_621] :
( in(ordered_pair(U_623,U_621),U_627)
| ~ in(ordered_pair(U_622,U_621),U_627)
| ~ in(ordered_pair(U_623,U_622),U_627) )
| ~ transitive(U_627) ) )
| ~ relation(U_627) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK108]),skolemize(U_626,sK108(U_627))],[f_143_2]) ).
fof(f_143_4,plain,
! [U_627] :
( ( ( transitive(U_627)
| ? [U_624] :
( ~ in(ordered_pair(sK108(U_627),U_624),U_627)
& in(ordered_pair(sK109(U_627),U_624),U_627)
& in(ordered_pair(sK108(U_627),sK109(U_627)),U_627) ) )
& ( ! [U_623,U_622,U_621] :
( in(ordered_pair(U_623,U_621),U_627)
| ~ in(ordered_pair(U_622,U_621),U_627)
| ~ in(ordered_pair(U_623,U_622),U_627) )
| ~ transitive(U_627) ) )
| ~ relation(U_627) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK109]),skolemize(U_625,sK109(U_627))],[f_143_3]) ).
fof(f_143_5,plain,
! [U_627] :
( ( ( transitive(U_627)
| ( ~ in(ordered_pair(sK108(U_627),sK110(U_627)),U_627)
& in(ordered_pair(sK109(U_627),sK110(U_627)),U_627)
& in(ordered_pair(sK108(U_627),sK109(U_627)),U_627) ) )
& ( ! [U_623,U_622,U_621] :
( in(ordered_pair(U_623,U_621),U_627)
| ~ in(ordered_pair(U_622,U_621),U_627)
| ~ in(ordered_pair(U_623,U_622),U_627) )
| ~ transitive(U_627) ) )
| ~ relation(U_627) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK110]),skolemize(U_624,sK110(U_627))],[f_143_4]) ).
cnf(f_143_6,plain,
( in(ordered_pair(U_623,U_621),U_627)
| ~ in(ordered_pair(U_622,U_621),U_627)
| ~ in(ordered_pair(U_623,U_622),U_627)
| ~ transitive(U_627)
| ~ relation(U_627) ),
inference(clausify,[status(thm)],[f_143_5]) ).
cnf(f_143_7,plain,
( in(ordered_pair(sK108(U_627),sK109(U_627)),U_627)
| transitive(U_627)
| ~ relation(U_627) ),
inference(clausify,[status(thm)],[f_143_5]) ).
cnf(f_143_8,plain,
( in(ordered_pair(sK109(U_627),sK110(U_627)),U_627)
| transitive(U_627)
| ~ relation(U_627) ),
inference(clausify,[status(thm)],[f_143_5]) ).
cnf(f_143_9,plain,
( ~ in(ordered_pair(sK108(U_627),sK110(U_627)),U_627)
| transitive(U_627)
| ~ relation(U_627) ),
inference(clausify,[status(thm)],[f_143_5]) ).
fof(f_144_1,plain,
! [A,B] :
( ( subset(singleton(A),B)
| ~ in(A,B) )
& ( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(fof_nnf,[status(thm)],[l2_zfmisc_1]) ).
fof(f_144_2,plain,
! [U_629,U_628] :
( ( subset(singleton(U_629),U_628)
| ~ in(U_629,U_628) )
& ( in(U_629,U_628)
| ~ subset(singleton(U_629),U_628) ) ),
inference(variable_rename,[status(thm)],[f_144_1]) ).
fof(f_144_3,plain,
( ! [U_633,U_631] :
( subset(singleton(U_633),U_631)
| ~ in(U_633,U_631) )
& ! [U_632,U_630] :
( in(U_632,U_630)
| ~ subset(singleton(U_632),U_630) ) ),
inference(miniscope,[status(thm)],[f_144_2]) ).
cnf(f_144_4,plain,
( in(U_632,U_630)
| ~ subset(singleton(U_632),U_630) ),
inference(clausify,[status(thm)],[f_144_3]) ).
cnf(f_144_5,plain,
( subset(singleton(U_633),U_631)
| ~ in(U_633,U_631) ),
inference(clausify,[status(thm)],[f_144_3]) ).
fof(f_145_1,plain,
! [A,B] :
( ( set_difference(A,B) = empty_set
| ~ subset(A,B) )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(fof_nnf,[status(thm)],[l32_xboole_1]) ).
fof(f_145_2,plain,
! [U_635,U_634] :
( ( set_difference(U_635,U_634) = empty_set
| ~ subset(U_635,U_634) )
& ( subset(U_635,U_634)
| set_difference(U_635,U_634) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_145_1]) ).
fof(f_145_3,plain,
( ! [U_639,U_637] :
( set_difference(U_639,U_637) = empty_set
| ~ subset(U_639,U_637) )
& ! [U_638,U_636] :
( subset(U_638,U_636)
| set_difference(U_638,U_636) != empty_set ) ),
inference(miniscope,[status(thm)],[f_145_2]) ).
cnf(f_145_4,plain,
( subset(U_638,U_636)
| set_difference(U_638,U_636) != empty_set ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_5,plain,
( set_difference(U_639,U_637) = empty_set
| ~ subset(U_639,U_637) ),
inference(clausify,[status(thm)],[f_145_3]) ).
fof(f_146_1,plain,
! [A,B] :
( ! [C] :
( in(C,A)
| ~ in(C,B) )
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[l3_subset_1]) ).
fof(f_146_2,plain,
! [U_642,U_641] :
( ! [U_640] :
( in(U_640,U_642)
| ~ in(U_640,U_641) )
| ~ element(U_641,powerset(U_642)) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
cnf(f_146_3,plain,
( in(U_640,U_642)
| ~ in(U_640,U_641)
| ~ element(U_641,powerset(U_642)) ),
inference(clausify,[status(thm)],[f_146_2]) ).
fof(f_147_1,plain,
! [A] :
( ( ( antisymmetric(A)
| ? [B,C] :
( B != C
& in(ordered_pair(C,B),A)
& in(ordered_pair(B,C),A) ) )
& ( ! [B,C] :
( B = C
| ~ in(ordered_pair(C,B),A)
| ~ in(ordered_pair(B,C),A) )
| ~ antisymmetric(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[l3_wellord1]) ).
fof(f_147_2,plain,
! [U_647] :
( ( ( antisymmetric(U_647)
| ? [U_646,U_645] :
( U_646 != U_645
& in(ordered_pair(U_645,U_646),U_647)
& in(ordered_pair(U_646,U_645),U_647) ) )
& ( ! [U_644,U_643] :
( U_644 = U_643
| ~ in(ordered_pair(U_643,U_644),U_647)
| ~ in(ordered_pair(U_644,U_643),U_647) )
| ~ antisymmetric(U_647) ) )
| ~ relation(U_647) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
fof(f_147_3,plain,
! [U_647] :
( ( ( antisymmetric(U_647)
| ? [U_645] :
( sK111(U_647) != U_645
& in(ordered_pair(U_645,sK111(U_647)),U_647)
& in(ordered_pair(sK111(U_647),U_645),U_647) ) )
& ( ! [U_644,U_643] :
( U_644 = U_643
| ~ in(ordered_pair(U_643,U_644),U_647)
| ~ in(ordered_pair(U_644,U_643),U_647) )
| ~ antisymmetric(U_647) ) )
| ~ relation(U_647) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK111]),skolemize(U_646,sK111(U_647))],[f_147_2]) ).
fof(f_147_4,plain,
! [U_647] :
( ( ( antisymmetric(U_647)
| ( sK111(U_647) != sK112(U_647)
& in(ordered_pair(sK112(U_647),sK111(U_647)),U_647)
& in(ordered_pair(sK111(U_647),sK112(U_647)),U_647) ) )
& ( ! [U_644,U_643] :
( U_644 = U_643
| ~ in(ordered_pair(U_643,U_644),U_647)
| ~ in(ordered_pair(U_644,U_643),U_647) )
| ~ antisymmetric(U_647) ) )
| ~ relation(U_647) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK112]),skolemize(U_645,sK112(U_647))],[f_147_3]) ).
cnf(f_147_5,plain,
( U_644 = U_643
| ~ in(ordered_pair(U_643,U_644),U_647)
| ~ in(ordered_pair(U_644,U_643),U_647)
| ~ antisymmetric(U_647)
| ~ relation(U_647) ),
inference(clausify,[status(thm)],[f_147_4]) ).
cnf(f_147_6,plain,
( in(ordered_pair(sK111(U_647),sK112(U_647)),U_647)
| antisymmetric(U_647)
| ~ relation(U_647) ),
inference(clausify,[status(thm)],[f_147_4]) ).
cnf(f_147_7,plain,
( in(ordered_pair(sK112(U_647),sK111(U_647)),U_647)
| antisymmetric(U_647)
| ~ relation(U_647) ),
inference(clausify,[status(thm)],[f_147_4]) ).
cnf(f_147_8,plain,
( sK111(U_647) != sK112(U_647)
| antisymmetric(U_647)
| ~ relation(U_647) ),
inference(clausify,[status(thm)],[f_147_4]) ).
fof(f_148_1,plain,
! [A,B,C] :
( subset(A,set_difference(B,singleton(C)))
| in(C,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[l3_zfmisc_1]) ).
fof(f_148_2,plain,
! [U_650,U_649,U_648] :
( subset(U_650,set_difference(U_649,singleton(U_648)))
| in(U_648,U_650)
| ~ subset(U_650,U_649) ),
inference(variable_rename,[status(thm)],[f_148_1]) ).
fof(f_148_3,plain,
! [U_650,U_649] :
( ! [U_648] :
( subset(U_650,set_difference(U_649,singleton(U_648)))
| in(U_648,U_650) )
| ~ subset(U_650,U_649) ),
inference(miniscope,[status(thm)],[f_148_2]) ).
cnf(f_148_4,plain,
( subset(U_650,set_difference(U_649,singleton(U_648)))
| in(U_648,U_650)
| ~ subset(U_650,U_649) ),
inference(clausify,[status(thm)],[f_148_3]) ).
fof(f_149_1,plain,
! [A] :
( ( ( connected(A)
| ? [B,C] :
( ~ in(ordered_pair(C,B),A)
& ~ in(ordered_pair(B,C),A)
& B != C
& in(C,relation_field(A))
& in(B,relation_field(A)) ) )
& ( ! [B,C] :
( in(ordered_pair(C,B),A)
| in(ordered_pair(B,C),A)
| B = C
| ~ in(C,relation_field(A))
| ~ in(B,relation_field(A)) )
| ~ connected(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[l4_wellord1]) ).
fof(f_149_2,plain,
! [U_655] :
( ( ( connected(U_655)
| ? [U_654,U_653] :
( ~ in(ordered_pair(U_653,U_654),U_655)
& ~ in(ordered_pair(U_654,U_653),U_655)
& U_654 != U_653
& in(U_653,relation_field(U_655))
& in(U_654,relation_field(U_655)) ) )
& ( ! [U_652,U_651] :
( in(ordered_pair(U_651,U_652),U_655)
| in(ordered_pair(U_652,U_651),U_655)
| U_652 = U_651
| ~ in(U_651,relation_field(U_655))
| ~ in(U_652,relation_field(U_655)) )
| ~ connected(U_655) ) )
| ~ relation(U_655) ),
inference(variable_rename,[status(thm)],[f_149_1]) ).
fof(f_149_3,plain,
! [U_655] :
( ( ( connected(U_655)
| ? [U_654] :
( ? [U_653] :
( ~ in(ordered_pair(U_653,U_654),U_655)
& ~ in(ordered_pair(U_654,U_653),U_655)
& U_654 != U_653
& in(U_653,relation_field(U_655)) )
& in(U_654,relation_field(U_655)) ) )
& ( ! [U_652] :
( ! [U_651] :
( in(ordered_pair(U_651,U_652),U_655)
| in(ordered_pair(U_652,U_651),U_655)
| U_652 = U_651
| ~ in(U_651,relation_field(U_655)) )
| ~ in(U_652,relation_field(U_655)) )
| ~ connected(U_655) ) )
| ~ relation(U_655) ),
inference(miniscope,[status(thm)],[f_149_2]) ).
fof(f_149_4,plain,
! [U_655] :
( ( ( connected(U_655)
| ( ? [U_653] :
( ~ in(ordered_pair(U_653,sK113(U_655)),U_655)
& ~ in(ordered_pair(sK113(U_655),U_653),U_655)
& sK113(U_655) != U_653
& in(U_653,relation_field(U_655)) )
& in(sK113(U_655),relation_field(U_655)) ) )
& ( ! [U_652] :
( ! [U_651] :
( in(ordered_pair(U_651,U_652),U_655)
| in(ordered_pair(U_652,U_651),U_655)
| U_652 = U_651
| ~ in(U_651,relation_field(U_655)) )
| ~ in(U_652,relation_field(U_655)) )
| ~ connected(U_655) ) )
| ~ relation(U_655) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK113]),skolemize(U_654,sK113(U_655))],[f_149_3]) ).
fof(f_149_5,plain,
! [U_655] :
( ( ( connected(U_655)
| ( ~ in(ordered_pair(sK114(U_655),sK113(U_655)),U_655)
& ~ in(ordered_pair(sK113(U_655),sK114(U_655)),U_655)
& sK113(U_655) != sK114(U_655)
& in(sK114(U_655),relation_field(U_655))
& in(sK113(U_655),relation_field(U_655)) ) )
& ( ! [U_652] :
( ! [U_651] :
( in(ordered_pair(U_651,U_652),U_655)
| in(ordered_pair(U_652,U_651),U_655)
| U_652 = U_651
| ~ in(U_651,relation_field(U_655)) )
| ~ in(U_652,relation_field(U_655)) )
| ~ connected(U_655) ) )
| ~ relation(U_655) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK114]),skolemize(U_653,sK114(U_655))],[f_149_4]) ).
cnf(f_149_6,plain,
( in(ordered_pair(U_651,U_652),U_655)
| in(ordered_pair(U_652,U_651),U_655)
| U_652 = U_651
| ~ in(U_651,relation_field(U_655))
| ~ in(U_652,relation_field(U_655))
| ~ connected(U_655)
| ~ relation(U_655) ),
inference(clausify,[status(thm)],[f_149_5]) ).
cnf(f_149_7,plain,
( in(sK113(U_655),relation_field(U_655))
| connected(U_655)
| ~ relation(U_655) ),
inference(clausify,[status(thm)],[f_149_5]) ).
cnf(f_149_8,plain,
( in(sK114(U_655),relation_field(U_655))
| connected(U_655)
| ~ relation(U_655) ),
inference(clausify,[status(thm)],[f_149_5]) ).
cnf(f_149_9,plain,
( sK113(U_655) != sK114(U_655)
| connected(U_655)
| ~ relation(U_655) ),
inference(clausify,[status(thm)],[f_149_5]) ).
cnf(f_149_10,plain,
( ~ in(ordered_pair(sK113(U_655),sK114(U_655)),U_655)
| connected(U_655)
| ~ relation(U_655) ),
inference(clausify,[status(thm)],[f_149_5]) ).
cnf(f_149_11,plain,
( ~ in(ordered_pair(sK114(U_655),sK113(U_655)),U_655)
| connected(U_655)
| ~ relation(U_655) ),
inference(clausify,[status(thm)],[f_149_5]) ).
fof(f_150_1,plain,
! [A,B] :
( ( subset(A,singleton(B))
| ( A != singleton(B)
& A != empty_set ) )
& ( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(fof_nnf,[status(thm)],[l4_zfmisc_1]) ).
fof(f_150_2,plain,
! [U_657,U_656] :
( ( subset(U_657,singleton(U_656))
| ( U_657 != singleton(U_656)
& U_657 != empty_set ) )
& ( U_657 = singleton(U_656)
| U_657 = empty_set
| ~ subset(U_657,singleton(U_656)) ) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
fof(f_150_3,plain,
( ! [U_661,U_659] :
( subset(U_661,singleton(U_659))
| ( U_661 != singleton(U_659)
& U_661 != empty_set ) )
& ! [U_660,U_658] :
( U_660 = singleton(U_658)
| U_660 = empty_set
| ~ subset(U_660,singleton(U_658)) ) ),
inference(miniscope,[status(thm)],[f_150_2]) ).
cnf(f_150_4,plain,
( U_660 = singleton(U_658)
| U_660 = empty_set
| ~ subset(U_660,singleton(U_658)) ),
inference(clausify,[status(thm)],[f_150_3]) ).
cnf(f_150_5,plain,
( U_661 != empty_set
| subset(U_661,singleton(U_659)) ),
inference(clausify,[status(thm)],[f_150_3]) ).
cnf(f_150_6,plain,
( U_661 != singleton(U_659)
| subset(U_661,singleton(U_659)) ),
inference(clausify,[status(thm)],[f_150_3]) ).
fof(f_151_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l50_zfmisc_1]) ).
fof(f_151_2,plain,
! [U_663,U_662] :
( subset(U_663,union(U_662))
| ~ in(U_663,U_662) ),
inference(variable_rename,[status(thm)],[f_151_1]) ).
cnf(f_151_3,plain,
( subset(U_663,union(U_662))
| ~ in(U_663,U_662) ),
inference(clausify,[status(thm)],[f_151_2]) ).
fof(f_152_1,plain,
! [A,B,C,D] :
( ( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(B,D)
| ~ in(A,C) )
& ( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(fof_nnf,[status(thm)],[l55_zfmisc_1]) ).
fof(f_152_2,plain,
! [U_667,U_666,U_665,U_664] :
( ( in(ordered_pair(U_667,U_666),cartesian_product2(U_665,U_664))
| ~ in(U_666,U_664)
| ~ in(U_667,U_665) )
& ( ( in(U_666,U_664)
& in(U_667,U_665) )
| ~ in(ordered_pair(U_667,U_666),cartesian_product2(U_665,U_664)) ) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
fof(f_152_3,plain,
( ! [U_675,U_673,U_671,U_669] :
( in(ordered_pair(U_675,U_673),cartesian_product2(U_671,U_669))
| ~ in(U_673,U_669)
| ~ in(U_675,U_671) )
& ! [U_674,U_672,U_670,U_668] :
( ( in(U_672,U_668)
& in(U_674,U_670) )
| ~ in(ordered_pair(U_674,U_672),cartesian_product2(U_670,U_668)) ) ),
inference(miniscope,[status(thm)],[f_152_2]) ).
cnf(f_152_4,plain,
( in(U_674,U_670)
| ~ in(ordered_pair(U_674,U_672),cartesian_product2(U_670,U_668)) ),
inference(clausify,[status(thm)],[f_152_3]) ).
cnf(f_152_5,plain,
( in(U_672,U_668)
| ~ in(ordered_pair(U_674,U_672),cartesian_product2(U_670,U_668)) ),
inference(clausify,[status(thm)],[f_152_3]) ).
cnf(f_152_6,plain,
( in(ordered_pair(U_675,U_673),cartesian_product2(U_671,U_669))
| ~ in(U_673,U_669)
| ~ in(U_675,U_671) ),
inference(clausify,[status(thm)],[f_152_3]) ).
fof(f_153_1,plain,
! [A,B] :
( element(A,powerset(B))
| ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(fof_nnf,[status(thm)],[l71_subset_1]) ).
fof(f_153_2,plain,
! [U_678,U_677] :
( element(U_678,powerset(U_677))
| ? [U_676] :
( ~ in(U_676,U_677)
& in(U_676,U_678) ) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
fof(f_153_3,plain,
! [U_678,U_677] :
( element(U_678,powerset(U_677))
| ( ~ in(sK115(U_678,U_677),U_677)
& in(sK115(U_678,U_677),U_678) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK115]),skolemize(U_676,sK115(U_678,U_677))],[f_153_2]) ).
cnf(f_153_4,plain,
( in(sK115(U_678,U_677),U_678)
| element(U_678,powerset(U_677)) ),
inference(clausify,[status(thm)],[f_153_3]) ).
cnf(f_153_5,plain,
( ~ in(sK115(U_678,U_677),U_677)
| element(U_678,powerset(U_677)) ),
inference(clausify,[status(thm)],[f_153_3]) ).
fof(f_154_1,plain,
! [A,B,C] :
( ( ( in(B,relation_dom(relation_dom_restriction(C,A)))
| ~ in(B,A)
| ~ in(B,relation_dom(C)) )
& ( ( in(B,A)
& in(B,relation_dom(C)) )
| ~ in(B,relation_dom(relation_dom_restriction(C,A))) ) )
| ~ function(C)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[l82_funct_1]) ).
fof(f_154_2,plain,
! [U_681,U_680,U_679] :
( ( ( in(U_680,relation_dom(relation_dom_restriction(U_679,U_681)))
| ~ in(U_680,U_681)
| ~ in(U_680,relation_dom(U_679)) )
& ( ( in(U_680,U_681)
& in(U_680,relation_dom(U_679)) )
| ~ in(U_680,relation_dom(relation_dom_restriction(U_679,U_681))) ) )
| ~ function(U_679)
| ~ relation(U_679) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
cnf(f_154_3,plain,
( in(U_680,relation_dom(U_679))
| ~ in(U_680,relation_dom(relation_dom_restriction(U_679,U_681)))
| ~ function(U_679)
| ~ relation(U_679) ),
inference(clausify,[status(thm)],[f_154_2]) ).
cnf(f_154_4,plain,
( in(U_680,U_681)
| ~ in(U_680,relation_dom(relation_dom_restriction(U_679,U_681)))
| ~ function(U_679)
| ~ relation(U_679) ),
inference(clausify,[status(thm)],[f_154_2]) ).
cnf(f_154_5,plain,
( in(U_680,relation_dom(relation_dom_restriction(U_679,U_681)))
| ~ in(U_680,U_681)
| ~ in(U_680,relation_dom(U_679))
| ~ function(U_679)
| ~ relation(U_679) ),
inference(clausify,[status(thm)],[f_154_2]) ).
fof(f_155_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_155_2,plain,
? [U_682] :
( function(U_682)
& relation(U_682) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
fof(f_155_3,plain,
( function(sK116)
& relation(sK116) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK116]),skolemize(U_682,sK116)],[f_155_2]) ).
cnf(f_155_4,plain,
relation(sK116),
inference(clausify,[status(thm)],[f_155_3]) ).
cnf(f_155_5,plain,
function(sK116),
inference(clausify,[status(thm)],[f_155_3]) ).
fof(f_156_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[rc1_ordinal1]) ).
fof(f_156_2,plain,
? [U_683] :
( ordinal(U_683)
& epsilon_connected(U_683)
& epsilon_transitive(U_683) ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
fof(f_156_3,plain,
( ordinal(sK117)
& epsilon_connected(sK117)
& epsilon_transitive(sK117) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK117]),skolemize(U_683,sK117)],[f_156_2]) ).
cnf(f_156_4,plain,
epsilon_transitive(sK117),
inference(clausify,[status(thm)],[f_156_3]) ).
cnf(f_156_5,plain,
epsilon_connected(sK117),
inference(clausify,[status(thm)],[f_156_3]) ).
cnf(f_156_6,plain,
ordinal(sK117),
inference(clausify,[status(thm)],[f_156_3]) ).
fof(f_157_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_157_2,plain,
? [U_684] :
( relation(U_684)
& empty(U_684) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
fof(f_157_3,plain,
( relation(sK118)
& empty(sK118) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK118]),skolemize(U_684,sK118)],[f_157_2]) ).
cnf(f_157_4,plain,
empty(sK118),
inference(clausify,[status(thm)],[f_157_3]) ).
cnf(f_157_5,plain,
relation(sK118),
inference(clausify,[status(thm)],[f_157_3]) ).
fof(f_158_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_158_2,plain,
! [U_686] :
( ? [U_685] :
( ~ empty(U_685)
& element(U_685,powerset(U_686)) )
| empty(U_686) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
fof(f_158_3,plain,
! [U_686] :
( ( ~ empty(sK119(U_686))
& element(sK119(U_686),powerset(U_686)) )
| empty(U_686) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK119]),skolemize(U_685,sK119(U_686))],[f_158_2]) ).
cnf(f_158_4,plain,
( element(sK119(U_686),powerset(U_686))
| empty(U_686) ),
inference(clausify,[status(thm)],[f_158_3]) ).
cnf(f_158_5,plain,
( ~ empty(sK119(U_686))
| empty(U_686) ),
inference(clausify,[status(thm)],[f_158_3]) ).
fof(f_159_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_159_2,plain,
? [U_687] : empty(U_687),
inference(variable_rename,[status(thm)],[f_159_1]) ).
fof(f_159_3,plain,
empty(sK120),
inference(skolemize,[status(esa),new_symbols(skolem,[sK120]),skolemize(U_687,sK120)],[f_159_2]) ).
cnf(f_159_4,plain,
empty(sK120),
inference(clausify,[status(thm)],[f_159_3]) ).
fof(f_160_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_160_2,plain,
? [U_688] :
( function(U_688)
& empty(U_688)
& relation(U_688) ),
inference(variable_rename,[status(thm)],[f_160_1]) ).
fof(f_160_3,plain,
( function(sK121)
& empty(sK121)
& relation(sK121) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK121]),skolemize(U_688,sK121)],[f_160_2]) ).
cnf(f_160_4,plain,
relation(sK121),
inference(clausify,[status(thm)],[f_160_3]) ).
cnf(f_160_5,plain,
empty(sK121),
inference(clausify,[status(thm)],[f_160_3]) ).
cnf(f_160_6,plain,
function(sK121),
inference(clausify,[status(thm)],[f_160_3]) ).
fof(f_161_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_ordinal1]) ).
fof(f_161_2,plain,
? [U_689] :
( ordinal(U_689)
& epsilon_connected(U_689)
& epsilon_transitive(U_689)
& empty(U_689)
& one_to_one(U_689)
& function(U_689)
& relation(U_689) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
fof(f_161_3,plain,
( ordinal(sK122)
& epsilon_connected(sK122)
& epsilon_transitive(sK122)
& empty(sK122)
& one_to_one(sK122)
& function(sK122)
& relation(sK122) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(U_689,sK122)],[f_161_2]) ).
cnf(f_161_4,plain,
relation(sK122),
inference(clausify,[status(thm)],[f_161_3]) ).
cnf(f_161_5,plain,
function(sK122),
inference(clausify,[status(thm)],[f_161_3]) ).
cnf(f_161_6,plain,
one_to_one(sK122),
inference(clausify,[status(thm)],[f_161_3]) ).
cnf(f_161_7,plain,
empty(sK122),
inference(clausify,[status(thm)],[f_161_3]) ).
cnf(f_161_8,plain,
epsilon_transitive(sK122),
inference(clausify,[status(thm)],[f_161_3]) ).
cnf(f_161_9,plain,
epsilon_connected(sK122),
inference(clausify,[status(thm)],[f_161_3]) ).
cnf(f_161_10,plain,
ordinal(sK122),
inference(clausify,[status(thm)],[f_161_3]) ).
fof(f_162_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_162_2,plain,
? [U_690] :
( relation(U_690)
& ~ empty(U_690) ),
inference(variable_rename,[status(thm)],[f_162_1]) ).
fof(f_162_3,plain,
( relation(sK123)
& ~ empty(sK123) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK123]),skolemize(U_690,sK123)],[f_162_2]) ).
cnf(f_162_4,plain,
~ empty(sK123),
inference(clausify,[status(thm)],[f_162_3]) ).
cnf(f_162_5,plain,
relation(sK123),
inference(clausify,[status(thm)],[f_162_3]) ).
fof(f_163_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_163_2,plain,
! [U_692] :
? [U_691] :
( empty(U_691)
& element(U_691,powerset(U_692)) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
fof(f_163_3,plain,
! [U_692] :
( empty(sK124(U_692))
& element(sK124(U_692),powerset(U_692)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK124]),skolemize(U_691,sK124(U_692))],[f_163_2]) ).
cnf(f_163_4,plain,
element(sK124(U_692),powerset(U_692)),
inference(clausify,[status(thm)],[f_163_3]) ).
cnf(f_163_5,plain,
empty(sK124(U_692)),
inference(clausify,[status(thm)],[f_163_3]) ).
fof(f_164_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_164_2,plain,
? [U_693] : ~ empty(U_693),
inference(variable_rename,[status(thm)],[f_164_1]) ).
fof(f_164_3,plain,
~ empty(sK125),
inference(skolemize,[status(esa),new_symbols(skolem,[sK125]),skolemize(U_693,sK125)],[f_164_2]) ).
cnf(f_164_4,plain,
~ empty(sK125),
inference(clausify,[status(thm)],[f_164_3]) ).
fof(f_165_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_165_2,plain,
? [U_694] :
( one_to_one(U_694)
& function(U_694)
& relation(U_694) ),
inference(variable_rename,[status(thm)],[f_165_1]) ).
fof(f_165_3,plain,
( one_to_one(sK126)
& function(sK126)
& relation(sK126) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK126]),skolemize(U_694,sK126)],[f_165_2]) ).
cnf(f_165_4,plain,
relation(sK126),
inference(clausify,[status(thm)],[f_165_3]) ).
cnf(f_165_5,plain,
function(sK126),
inference(clausify,[status(thm)],[f_165_3]) ).
cnf(f_165_6,plain,
one_to_one(sK126),
inference(clausify,[status(thm)],[f_165_3]) ).
fof(f_166_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_ordinal1]) ).
fof(f_166_2,plain,
? [U_695] :
( ordinal(U_695)
& epsilon_connected(U_695)
& epsilon_transitive(U_695)
& ~ empty(U_695) ),
inference(variable_rename,[status(thm)],[f_166_1]) ).
fof(f_166_3,plain,
( ordinal(sK127)
& epsilon_connected(sK127)
& epsilon_transitive(sK127)
& ~ empty(sK127) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK127]),skolemize(U_695,sK127)],[f_166_2]) ).
cnf(f_166_4,plain,
~ empty(sK127),
inference(clausify,[status(thm)],[f_166_3]) ).
cnf(f_166_5,plain,
epsilon_transitive(sK127),
inference(clausify,[status(thm)],[f_166_3]) ).
cnf(f_166_6,plain,
epsilon_connected(sK127),
inference(clausify,[status(thm)],[f_166_3]) ).
cnf(f_166_7,plain,
ordinal(sK127),
inference(clausify,[status(thm)],[f_166_3]) ).
fof(f_167_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_167_2,plain,
? [U_696] :
( relation_empty_yielding(U_696)
& relation(U_696) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
fof(f_167_3,plain,
( relation_empty_yielding(sK128)
& relation(sK128) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK128]),skolemize(U_696,sK128)],[f_167_2]) ).
cnf(f_167_4,plain,
relation(sK128),
inference(clausify,[status(thm)],[f_167_3]) ).
cnf(f_167_5,plain,
relation_empty_yielding(sK128),
inference(clausify,[status(thm)],[f_167_3]) ).
fof(f_168_1,plain,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc4_funct_1]) ).
fof(f_168_2,plain,
? [U_697] :
( function(U_697)
& relation_empty_yielding(U_697)
& relation(U_697) ),
inference(variable_rename,[status(thm)],[f_168_1]) ).
fof(f_168_3,plain,
( function(sK129)
& relation_empty_yielding(sK129)
& relation(sK129) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK129]),skolemize(U_697,sK129)],[f_168_2]) ).
cnf(f_168_4,plain,
relation(sK129),
inference(clausify,[status(thm)],[f_168_3]) ).
cnf(f_168_5,plain,
relation_empty_yielding(sK129),
inference(clausify,[status(thm)],[f_168_3]) ).
cnf(f_168_6,plain,
function(sK129),
inference(clausify,[status(thm)],[f_168_3]) ).
fof(f_169_1,plain,
! [A,B] :
( union_of_subsets(A,B) = union(B)
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[redefinition_k5_setfam_1]) ).
fof(f_169_2,plain,
! [U_699,U_698] :
( union_of_subsets(U_699,U_698) = union(U_698)
| ~ element(U_698,powerset(powerset(U_699))) ),
inference(variable_rename,[status(thm)],[f_169_1]) ).
cnf(f_169_3,plain,
( union_of_subsets(U_699,U_698) = union(U_698)
| ~ element(U_698,powerset(powerset(U_699))) ),
inference(clausify,[status(thm)],[f_169_2]) ).
fof(f_170_1,plain,
! [A,B] :
( meet_of_subsets(A,B) = set_meet(B)
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[redefinition_k6_setfam_1]) ).
fof(f_170_2,plain,
! [U_701,U_700] :
( meet_of_subsets(U_701,U_700) = set_meet(U_700)
| ~ element(U_700,powerset(powerset(U_701))) ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
cnf(f_170_3,plain,
( meet_of_subsets(U_701,U_700) = set_meet(U_700)
| ~ element(U_700,powerset(powerset(U_701))) ),
inference(clausify,[status(thm)],[f_170_2]) ).
fof(f_171_1,plain,
! [A,B,C] :
( subset_difference(A,B,C) = set_difference(B,C)
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[redefinition_k6_subset_1]) ).
fof(f_171_2,plain,
! [U_704,U_703,U_702] :
( subset_difference(U_704,U_703,U_702) = set_difference(U_703,U_702)
| ~ element(U_702,powerset(U_704))
| ~ element(U_703,powerset(U_704)) ),
inference(variable_rename,[status(thm)],[f_171_1]) ).
cnf(f_171_3,plain,
( subset_difference(U_704,U_703,U_702) = set_difference(U_703,U_702)
| ~ element(U_702,powerset(U_704))
| ~ element(U_703,powerset(U_704)) ),
inference(clausify,[status(thm)],[f_171_2]) ).
fof(f_172_1,plain,
! [A,B] :
( ( ( ordinal_subset(A,B)
| ~ subset(A,B) )
& ( subset(A,B)
| ~ ordinal_subset(A,B) ) )
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[redefinition_r1_ordinal1]) ).
fof(f_172_2,plain,
! [U_706,U_705] :
( ( ( ordinal_subset(U_706,U_705)
| ~ subset(U_706,U_705) )
& ( subset(U_706,U_705)
| ~ ordinal_subset(U_706,U_705) ) )
| ~ ordinal(U_705)
| ~ ordinal(U_706) ),
inference(variable_rename,[status(thm)],[f_172_1]) ).
cnf(f_172_3,plain,
( subset(U_706,U_705)
| ~ ordinal_subset(U_706,U_705)
| ~ ordinal(U_705)
| ~ ordinal(U_706) ),
inference(clausify,[status(thm)],[f_172_2]) ).
cnf(f_172_4,plain,
( ordinal_subset(U_706,U_705)
| ~ subset(U_706,U_705)
| ~ ordinal(U_705)
| ~ ordinal(U_706) ),
inference(clausify,[status(thm)],[f_172_2]) ).
fof(f_173_1,plain,
! [A,B] :
( ordinal_subset(A,A)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[reflexivity_r1_ordinal1]) ).
fof(f_173_2,plain,
! [U_708,U_707] :
( ordinal_subset(U_708,U_708)
| ~ ordinal(U_707)
| ~ ordinal(U_708) ),
inference(variable_rename,[status(thm)],[f_173_1]) ).
fof(f_173_3,plain,
! [U_708] :
( ! [U_707] : ~ ordinal(U_707)
| ~ ordinal(U_708)
| ordinal_subset(U_708,U_708) ),
inference(miniscope,[status(thm)],[f_173_2]) ).
cnf(f_173_4,plain,
( ~ ordinal(U_707)
| ~ ordinal(U_708)
| ordinal_subset(U_708,U_708) ),
inference(clausify,[status(thm)],[f_173_3]) ).
fof(f_174_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_174_2,plain,
! [U_710,U_709] : subset(U_710,U_710),
inference(variable_rename,[status(thm)],[f_174_1]) ).
fof(f_174_3,plain,
! [U_710] : subset(U_710,U_710),
inference(miniscope,[status(thm)],[f_174_2]) ).
cnf(f_174_4,plain,
subset(U_710,U_710),
inference(clausify,[status(thm)],[f_174_3]) ).
fof(f_175_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_175_2,plain,
! [U_712,U_711] :
( disjoint(U_711,U_712)
| ~ disjoint(U_712,U_711) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
cnf(f_175_3,plain,
( disjoint(U_711,U_712)
| ~ disjoint(U_712,U_711) ),
inference(clausify,[status(thm)],[f_175_2]) ).
fof(f_176_1,plain,
! [A,B,C,D] :
( ( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(B,D)
| ~ in(A,C) )
& ( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(fof_nnf,[status(thm)],[t106_zfmisc_1]) ).
fof(f_176_2,plain,
! [U_716,U_715,U_714,U_713] :
( ( in(ordered_pair(U_716,U_715),cartesian_product2(U_714,U_713))
| ~ in(U_715,U_713)
| ~ in(U_716,U_714) )
& ( ( in(U_715,U_713)
& in(U_716,U_714) )
| ~ in(ordered_pair(U_716,U_715),cartesian_product2(U_714,U_713)) ) ),
inference(variable_rename,[status(thm)],[f_176_1]) ).
fof(f_176_3,plain,
( ! [U_724,U_722,U_720,U_718] :
( in(ordered_pair(U_724,U_722),cartesian_product2(U_720,U_718))
| ~ in(U_722,U_718)
| ~ in(U_724,U_720) )
& ! [U_723,U_721,U_719,U_717] :
( ( in(U_721,U_717)
& in(U_723,U_719) )
| ~ in(ordered_pair(U_723,U_721),cartesian_product2(U_719,U_717)) ) ),
inference(miniscope,[status(thm)],[f_176_2]) ).
cnf(f_176_4,plain,
( in(U_723,U_719)
| ~ in(ordered_pair(U_723,U_721),cartesian_product2(U_719,U_717)) ),
inference(clausify,[status(thm)],[f_176_3]) ).
cnf(f_176_5,plain,
( in(U_721,U_717)
| ~ in(ordered_pair(U_723,U_721),cartesian_product2(U_719,U_717)) ),
inference(clausify,[status(thm)],[f_176_3]) ).
cnf(f_176_6,plain,
( in(ordered_pair(U_724,U_722),cartesian_product2(U_720,U_718))
| ~ in(U_722,U_718)
| ~ in(U_724,U_720) ),
inference(clausify,[status(thm)],[f_176_3]) ).
fof(f_177_1,plain,
! [A] : in(A,succ(A)),
inference(fof_nnf,[status(thm)],[t10_ordinal1]) ).
fof(f_177_2,plain,
! [U_725] : in(U_725,succ(U_725)),
inference(variable_rename,[status(thm)],[f_177_1]) ).
cnf(f_177_3,plain,
in(U_725,succ(U_725)),
inference(clausify,[status(thm)],[f_177_2]) ).
fof(f_178_1,plain,
! [A,B,C,D] :
( A = D
| A = C
| unordered_pair(A,B) != unordered_pair(C,D) ),
inference(fof_nnf,[status(thm)],[t10_zfmisc_1]) ).
fof(f_178_2,plain,
! [U_729,U_728,U_727,U_726] :
( U_729 = U_726
| U_729 = U_727
| unordered_pair(U_729,U_728) != unordered_pair(U_727,U_726) ),
inference(variable_rename,[status(thm)],[f_178_1]) ).
fof(f_178_3,plain,
! [U_729,U_728,U_727] :
( ! [U_726] :
( U_729 = U_726
| unordered_pair(U_729,U_728) != unordered_pair(U_727,U_726) )
| U_729 = U_727 ),
inference(miniscope,[status(thm)],[f_178_2]) ).
cnf(f_178_4,plain,
( U_729 = U_726
| unordered_pair(U_729,U_728) != unordered_pair(U_727,U_726)
| U_729 = U_727 ),
inference(clausify,[status(thm)],[f_178_3]) ).
fof(f_179_1,plain,
! [A,B,C] :
( ( ( in(A,relation_rng(relation_rng_restriction(B,C)))
| ~ in(A,relation_rng(C))
| ~ in(A,B) )
& ( ( in(A,relation_rng(C))
& in(A,B) )
| ~ in(A,relation_rng(relation_rng_restriction(B,C))) ) )
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t115_relat_1]) ).
fof(f_179_2,plain,
! [U_732,U_731,U_730] :
( ( ( in(U_732,relation_rng(relation_rng_restriction(U_731,U_730)))
| ~ in(U_732,relation_rng(U_730))
| ~ in(U_732,U_731) )
& ( ( in(U_732,relation_rng(U_730))
& in(U_732,U_731) )
| ~ in(U_732,relation_rng(relation_rng_restriction(U_731,U_730))) ) )
| ~ relation(U_730) ),
inference(variable_rename,[status(thm)],[f_179_1]) ).
cnf(f_179_3,plain,
( in(U_732,U_731)
| ~ in(U_732,relation_rng(relation_rng_restriction(U_731,U_730)))
| ~ relation(U_730) ),
inference(clausify,[status(thm)],[f_179_2]) ).
cnf(f_179_4,plain,
( in(U_732,relation_rng(U_730))
| ~ in(U_732,relation_rng(relation_rng_restriction(U_731,U_730)))
| ~ relation(U_730) ),
inference(clausify,[status(thm)],[f_179_2]) ).
cnf(f_179_5,plain,
( in(U_732,relation_rng(relation_rng_restriction(U_731,U_730)))
| ~ in(U_732,relation_rng(U_730))
| ~ in(U_732,U_731)
| ~ relation(U_730) ),
inference(clausify,[status(thm)],[f_179_2]) ).
fof(f_180_1,plain,
! [A,B] :
( subset(relation_rng(relation_rng_restriction(A,B)),A)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t116_relat_1]) ).
fof(f_180_2,plain,
! [U_734,U_733] :
( subset(relation_rng(relation_rng_restriction(U_734,U_733)),U_734)
| ~ relation(U_733) ),
inference(variable_rename,[status(thm)],[f_180_1]) ).
cnf(f_180_3,plain,
( subset(relation_rng(relation_rng_restriction(U_734,U_733)),U_734)
| ~ relation(U_733) ),
inference(clausify,[status(thm)],[f_180_2]) ).
fof(f_181_1,plain,
! [A,B] :
( subset(relation_rng_restriction(A,B),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t117_relat_1]) ).
fof(f_181_2,plain,
! [U_736,U_735] :
( subset(relation_rng_restriction(U_736,U_735),U_735)
| ~ relation(U_735) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
cnf(f_181_3,plain,
( subset(relation_rng_restriction(U_736,U_735),U_735)
| ~ relation(U_735) ),
inference(clausify,[status(thm)],[f_181_2]) ).
fof(f_182_1,plain,
! [A,B] :
( subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t118_relat_1]) ).
fof(f_182_2,plain,
! [U_738,U_737] :
( subset(relation_rng(relation_rng_restriction(U_738,U_737)),relation_rng(U_737))
| ~ relation(U_737) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
cnf(f_182_3,plain,
( subset(relation_rng(relation_rng_restriction(U_738,U_737)),relation_rng(U_737))
| ~ relation(U_737) ),
inference(clausify,[status(thm)],[f_182_2]) ).
fof(f_183_1,plain,
! [A,B,C] :
( ( subset(cartesian_product2(C,A),cartesian_product2(C,B))
& subset(cartesian_product2(A,C),cartesian_product2(B,C)) )
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t118_zfmisc_1]) ).
fof(f_183_2,plain,
! [U_741,U_740,U_739] :
( ( subset(cartesian_product2(U_739,U_741),cartesian_product2(U_739,U_740))
& subset(cartesian_product2(U_741,U_739),cartesian_product2(U_740,U_739)) )
| ~ subset(U_741,U_740) ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
fof(f_183_3,plain,
! [U_741,U_740] :
( ( ! [U_743] : subset(cartesian_product2(U_743,U_741),cartesian_product2(U_743,U_740))
& ! [U_742] : subset(cartesian_product2(U_741,U_742),cartesian_product2(U_740,U_742)) )
| ~ subset(U_741,U_740) ),
inference(miniscope,[status(thm)],[f_183_2]) ).
cnf(f_183_4,plain,
( subset(cartesian_product2(U_741,U_742),cartesian_product2(U_740,U_742))
| ~ subset(U_741,U_740) ),
inference(clausify,[status(thm)],[f_183_3]) ).
cnf(f_183_5,plain,
( subset(cartesian_product2(U_743,U_741),cartesian_product2(U_743,U_740))
| ~ subset(U_741,U_740) ),
inference(clausify,[status(thm)],[f_183_3]) ).
fof(f_184_1,plain,
! [A,B] :
( relation_rng(relation_rng_restriction(A,B)) = set_intersection2(relation_rng(B),A)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t119_relat_1]) ).
fof(f_184_2,plain,
! [U_745,U_744] :
( relation_rng(relation_rng_restriction(U_745,U_744)) = set_intersection2(relation_rng(U_744),U_745)
| ~ relation(U_744) ),
inference(variable_rename,[status(thm)],[f_184_1]) ).
cnf(f_184_3,plain,
( relation_rng(relation_rng_restriction(U_745,U_744)) = set_intersection2(relation_rng(U_744),U_745)
| ~ relation(U_744) ),
inference(clausify,[status(thm)],[f_184_2]) ).
fof(f_185_1,plain,
! [A,B,C,D] :
( subset(cartesian_product2(A,C),cartesian_product2(B,D))
| ~ subset(C,D)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t119_zfmisc_1]) ).
fof(f_185_2,plain,
! [U_749,U_748,U_747,U_746] :
( subset(cartesian_product2(U_749,U_747),cartesian_product2(U_748,U_746))
| ~ subset(U_747,U_746)
| ~ subset(U_749,U_748) ),
inference(variable_rename,[status(thm)],[f_185_1]) ).
cnf(f_185_3,plain,
( subset(cartesian_product2(U_749,U_747),cartesian_product2(U_748,U_746))
| ~ subset(U_747,U_746)
| ~ subset(U_749,U_748) ),
inference(clausify,[status(thm)],[f_185_2]) ).
fof(f_186_1,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t12_xboole_1]) ).
fof(f_186_2,plain,
! [U_751,U_750] :
( set_union2(U_751,U_750) = U_750
| ~ subset(U_751,U_750) ),
inference(variable_rename,[status(thm)],[f_186_1]) ).
cnf(f_186_3,plain,
( set_union2(U_751,U_750) = U_750
| ~ subset(U_751,U_750) ),
inference(clausify,[status(thm)],[f_186_2]) ).
fof(f_187_1,plain,
! [A] :
? [B] :
( ! [C] :
( in(C,B)
| are_equipotent(C,B)
| ~ subset(C,B) )
& ! [C] :
( in(powerset(C),B)
| ~ in(C,B) )
& ! [C,D] :
( in(D,B)
| ~ subset(D,C)
| ~ in(C,B) )
& in(A,B) ),
inference(fof_nnf,[status(thm)],[t136_zfmisc_1]) ).
fof(f_187_2,plain,
! [U_757] :
? [U_756] :
( ! [U_755] :
( in(U_755,U_756)
| are_equipotent(U_755,U_756)
| ~ subset(U_755,U_756) )
& ! [U_754] :
( in(powerset(U_754),U_756)
| ~ in(U_754,U_756) )
& ! [U_753,U_752] :
( in(U_752,U_756)
| ~ subset(U_752,U_753)
| ~ in(U_753,U_756) )
& in(U_757,U_756) ),
inference(variable_rename,[status(thm)],[f_187_1]) ).
fof(f_187_3,plain,
! [U_757] :
( ! [U_755] :
( in(U_755,sK130(U_757))
| are_equipotent(U_755,sK130(U_757))
| ~ subset(U_755,sK130(U_757)) )
& ! [U_754] :
( in(powerset(U_754),sK130(U_757))
| ~ in(U_754,sK130(U_757)) )
& ! [U_753,U_752] :
( in(U_752,sK130(U_757))
| ~ subset(U_752,U_753)
| ~ in(U_753,sK130(U_757)) )
& in(U_757,sK130(U_757)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK130]),skolemize(U_756,sK130(U_757))],[f_187_2]) ).
cnf(f_187_4,plain,
in(U_757,sK130(U_757)),
inference(clausify,[status(thm)],[f_187_3]) ).
cnf(f_187_5,plain,
( in(U_752,sK130(U_757))
| ~ subset(U_752,U_753)
| ~ in(U_753,sK130(U_757)) ),
inference(clausify,[status(thm)],[f_187_3]) ).
cnf(f_187_6,plain,
( in(powerset(U_754),sK130(U_757))
| ~ in(U_754,sK130(U_757)) ),
inference(clausify,[status(thm)],[f_187_3]) ).
cnf(f_187_7,plain,
( in(U_755,sK130(U_757))
| are_equipotent(U_755,sK130(U_757))
| ~ subset(U_755,sK130(U_757)) ),
inference(clausify,[status(thm)],[f_187_3]) ).
fof(f_188_1,plain,
! [A,B,C] :
( relation_dom_restriction(relation_rng_restriction(A,C),B) = relation_rng_restriction(A,relation_dom_restriction(C,B))
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t140_relat_1]) ).
fof(f_188_2,plain,
! [U_760,U_759,U_758] :
( relation_dom_restriction(relation_rng_restriction(U_760,U_758),U_759) = relation_rng_restriction(U_760,relation_dom_restriction(U_758,U_759))
| ~ relation(U_758) ),
inference(variable_rename,[status(thm)],[f_188_1]) ).
cnf(f_188_3,plain,
( relation_dom_restriction(relation_rng_restriction(U_760,U_758),U_759) = relation_rng_restriction(U_760,relation_dom_restriction(U_758,U_759))
| ~ relation(U_758) ),
inference(clausify,[status(thm)],[f_188_2]) ).
fof(f_189_1,plain,
! [A,B,C] :
( ( ( in(A,relation_image(C,B))
| ! [D] :
( ~ in(D,B)
| ~ in(ordered_pair(D,A),C)
| ~ in(D,relation_dom(C)) ) )
& ( ? [D] :
( in(D,B)
& in(ordered_pair(D,A),C)
& in(D,relation_dom(C)) )
| ~ in(A,relation_image(C,B)) ) )
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t143_relat_1]) ).
fof(f_189_2,plain,
! [U_765,U_764,U_763] :
( ( ( in(U_765,relation_image(U_763,U_764))
| ! [U_762] :
( ~ in(U_762,U_764)
| ~ in(ordered_pair(U_762,U_765),U_763)
| ~ in(U_762,relation_dom(U_763)) ) )
& ( ? [U_761] :
( in(U_761,U_764)
& in(ordered_pair(U_761,U_765),U_763)
& in(U_761,relation_dom(U_763)) )
| ~ in(U_765,relation_image(U_763,U_764)) ) )
| ~ relation(U_763) ),
inference(variable_rename,[status(thm)],[f_189_1]) ).
fof(f_189_3,plain,
! [U_765,U_764,U_763] :
( ( ( in(U_765,relation_image(U_763,U_764))
| ! [U_762] :
( ~ in(U_762,U_764)
| ~ in(ordered_pair(U_762,U_765),U_763)
| ~ in(U_762,relation_dom(U_763)) ) )
& ( ( in(sK131(U_765,U_764,U_763),U_764)
& in(ordered_pair(sK131(U_765,U_764,U_763),U_765),U_763)
& in(sK131(U_765,U_764,U_763),relation_dom(U_763)) )
| ~ in(U_765,relation_image(U_763,U_764)) ) )
| ~ relation(U_763) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK131]),skolemize(U_761,sK131(U_765,U_764,U_763))],[f_189_2]) ).
cnf(f_189_4,plain,
( in(sK131(U_765,U_764,U_763),relation_dom(U_763))
| ~ in(U_765,relation_image(U_763,U_764))
| ~ relation(U_763) ),
inference(clausify,[status(thm)],[f_189_3]) ).
cnf(f_189_5,plain,
( in(ordered_pair(sK131(U_765,U_764,U_763),U_765),U_763)
| ~ in(U_765,relation_image(U_763,U_764))
| ~ relation(U_763) ),
inference(clausify,[status(thm)],[f_189_3]) ).
cnf(f_189_6,plain,
( in(sK131(U_765,U_764,U_763),U_764)
| ~ in(U_765,relation_image(U_763,U_764))
| ~ relation(U_763) ),
inference(clausify,[status(thm)],[f_189_3]) ).
cnf(f_189_7,plain,
( in(U_765,relation_image(U_763,U_764))
| ~ in(U_762,U_764)
| ~ in(ordered_pair(U_762,U_765),U_763)
| ~ in(U_762,relation_dom(U_763))
| ~ relation(U_763) ),
inference(clausify,[status(thm)],[f_189_3]) ).
fof(f_190_1,plain,
! [A,B] :
( subset(relation_image(B,A),relation_rng(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t144_relat_1]) ).
fof(f_190_2,plain,
! [U_767,U_766] :
( subset(relation_image(U_766,U_767),relation_rng(U_766))
| ~ relation(U_766) ),
inference(variable_rename,[status(thm)],[f_190_1]) ).
cnf(f_190_3,plain,
( subset(relation_image(U_766,U_767),relation_rng(U_766))
| ~ relation(U_766) ),
inference(clausify,[status(thm)],[f_190_2]) ).
fof(f_191_1,plain,
! [A,B] :
( subset(relation_image(B,relation_inverse_image(B,A)),A)
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t145_funct_1]) ).
fof(f_191_2,plain,
! [U_769,U_768] :
( subset(relation_image(U_768,relation_inverse_image(U_768,U_769)),U_769)
| ~ function(U_768)
| ~ relation(U_768) ),
inference(variable_rename,[status(thm)],[f_191_1]) ).
cnf(f_191_3,plain,
( subset(relation_image(U_768,relation_inverse_image(U_768,U_769)),U_769)
| ~ function(U_768)
| ~ relation(U_768) ),
inference(clausify,[status(thm)],[f_191_2]) ).
fof(f_192_1,plain,
! [A,B] :
( relation_image(B,A) = relation_image(B,set_intersection2(relation_dom(B),A))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t145_relat_1]) ).
fof(f_192_2,plain,
! [U_771,U_770] :
( relation_image(U_770,U_771) = relation_image(U_770,set_intersection2(relation_dom(U_770),U_771))
| ~ relation(U_770) ),
inference(variable_rename,[status(thm)],[f_192_1]) ).
cnf(f_192_3,plain,
( relation_image(U_770,U_771) = relation_image(U_770,set_intersection2(relation_dom(U_770),U_771))
| ~ relation(U_770) ),
inference(clausify,[status(thm)],[f_192_2]) ).
fof(f_193_1,plain,
! [A,B] :
( subset(A,relation_inverse_image(B,relation_image(B,A)))
| ~ subset(A,relation_dom(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t146_funct_1]) ).
fof(f_193_2,plain,
! [U_773,U_772] :
( subset(U_773,relation_inverse_image(U_772,relation_image(U_772,U_773)))
| ~ subset(U_773,relation_dom(U_772))
| ~ relation(U_772) ),
inference(variable_rename,[status(thm)],[f_193_1]) ).
cnf(f_193_3,plain,
( subset(U_773,relation_inverse_image(U_772,relation_image(U_772,U_773)))
| ~ subset(U_773,relation_dom(U_772))
| ~ relation(U_772) ),
inference(clausify,[status(thm)],[f_193_2]) ).
fof(f_194_1,plain,
! [A] :
( relation_image(A,relation_dom(A)) = relation_rng(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t146_relat_1]) ).
fof(f_194_2,plain,
! [U_774] :
( relation_image(U_774,relation_dom(U_774)) = relation_rng(U_774)
| ~ relation(U_774) ),
inference(variable_rename,[status(thm)],[f_194_1]) ).
cnf(f_194_3,plain,
( relation_image(U_774,relation_dom(U_774)) = relation_rng(U_774)
| ~ relation(U_774) ),
inference(clausify,[status(thm)],[f_194_2]) ).
fof(f_195_1,plain,
! [A,B] :
( relation_image(B,relation_inverse_image(B,A)) = A
| ~ subset(A,relation_rng(B))
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t147_funct_1]) ).
fof(f_195_2,plain,
! [U_776,U_775] :
( relation_image(U_775,relation_inverse_image(U_775,U_776)) = U_776
| ~ subset(U_776,relation_rng(U_775))
| ~ function(U_775)
| ~ relation(U_775) ),
inference(variable_rename,[status(thm)],[f_195_1]) ).
cnf(f_195_3,plain,
( relation_image(U_775,relation_inverse_image(U_775,U_776)) = U_776
| ~ subset(U_776,relation_rng(U_775))
| ~ function(U_775)
| ~ relation(U_775) ),
inference(clausify,[status(thm)],[f_195_2]) ).
fof(f_196_1,plain,
! [A] :
( ! [B] :
( relation_rng(relation_composition(A,B)) = relation_image(B,relation_rng(A))
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t160_relat_1]) ).
fof(f_196_2,plain,
! [U_778] :
( ! [U_777] :
( relation_rng(relation_composition(U_778,U_777)) = relation_image(U_777,relation_rng(U_778))
| ~ relation(U_777) )
| ~ relation(U_778) ),
inference(variable_rename,[status(thm)],[f_196_1]) ).
cnf(f_196_3,plain,
( relation_rng(relation_composition(U_778,U_777)) = relation_image(U_777,relation_rng(U_778))
| ~ relation(U_777)
| ~ relation(U_778) ),
inference(clausify,[status(thm)],[f_196_2]) ).
fof(f_197_1,plain,
! [A,B,C] :
( ( ( in(A,relation_inverse_image(C,B))
| ! [D] :
( ~ in(D,B)
| ~ in(ordered_pair(A,D),C)
| ~ in(D,relation_rng(C)) ) )
& ( ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) )
| ~ in(A,relation_inverse_image(C,B)) ) )
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t166_relat_1]) ).
fof(f_197_2,plain,
! [U_783,U_782,U_781] :
( ( ( in(U_783,relation_inverse_image(U_781,U_782))
| ! [U_780] :
( ~ in(U_780,U_782)
| ~ in(ordered_pair(U_783,U_780),U_781)
| ~ in(U_780,relation_rng(U_781)) ) )
& ( ? [U_779] :
( in(U_779,U_782)
& in(ordered_pair(U_783,U_779),U_781)
& in(U_779,relation_rng(U_781)) )
| ~ in(U_783,relation_inverse_image(U_781,U_782)) ) )
| ~ relation(U_781) ),
inference(variable_rename,[status(thm)],[f_197_1]) ).
fof(f_197_3,plain,
! [U_783,U_782,U_781] :
( ( ( in(U_783,relation_inverse_image(U_781,U_782))
| ! [U_780] :
( ~ in(U_780,U_782)
| ~ in(ordered_pair(U_783,U_780),U_781)
| ~ in(U_780,relation_rng(U_781)) ) )
& ( ( in(sK132(U_783,U_782,U_781),U_782)
& in(ordered_pair(U_783,sK132(U_783,U_782,U_781)),U_781)
& in(sK132(U_783,U_782,U_781),relation_rng(U_781)) )
| ~ in(U_783,relation_inverse_image(U_781,U_782)) ) )
| ~ relation(U_781) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK132]),skolemize(U_779,sK132(U_783,U_782,U_781))],[f_197_2]) ).
cnf(f_197_4,plain,
( in(sK132(U_783,U_782,U_781),relation_rng(U_781))
| ~ in(U_783,relation_inverse_image(U_781,U_782))
| ~ relation(U_781) ),
inference(clausify,[status(thm)],[f_197_3]) ).
cnf(f_197_5,plain,
( in(ordered_pair(U_783,sK132(U_783,U_782,U_781)),U_781)
| ~ in(U_783,relation_inverse_image(U_781,U_782))
| ~ relation(U_781) ),
inference(clausify,[status(thm)],[f_197_3]) ).
cnf(f_197_6,plain,
( in(sK132(U_783,U_782,U_781),U_782)
| ~ in(U_783,relation_inverse_image(U_781,U_782))
| ~ relation(U_781) ),
inference(clausify,[status(thm)],[f_197_3]) ).
cnf(f_197_7,plain,
( in(U_783,relation_inverse_image(U_781,U_782))
| ~ in(U_780,U_782)
| ~ in(ordered_pair(U_783,U_780),U_781)
| ~ in(U_780,relation_rng(U_781))
| ~ relation(U_781) ),
inference(clausify,[status(thm)],[f_197_3]) ).
fof(f_198_1,plain,
! [A,B] :
( subset(relation_inverse_image(B,A),relation_dom(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t167_relat_1]) ).
fof(f_198_2,plain,
! [U_785,U_784] :
( subset(relation_inverse_image(U_784,U_785),relation_dom(U_784))
| ~ relation(U_784) ),
inference(variable_rename,[status(thm)],[f_198_1]) ).
cnf(f_198_3,plain,
( subset(relation_inverse_image(U_784,U_785),relation_dom(U_784))
| ~ relation(U_784) ),
inference(clausify,[status(thm)],[f_198_2]) ).
fof(f_199_1,plain,
! [A,B] :
( relation_inverse_image(B,A) != empty_set
| ~ subset(A,relation_rng(B))
| A = empty_set
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t174_relat_1]) ).
fof(f_199_2,plain,
! [U_787,U_786] :
( relation_inverse_image(U_786,U_787) != empty_set
| ~ subset(U_787,relation_rng(U_786))
| U_787 = empty_set
| ~ relation(U_786) ),
inference(variable_rename,[status(thm)],[f_199_1]) ).
cnf(f_199_3,plain,
( relation_inverse_image(U_786,U_787) != empty_set
| ~ subset(U_787,relation_rng(U_786))
| U_787 = empty_set
| ~ relation(U_786) ),
inference(clausify,[status(thm)],[f_199_2]) ).
fof(f_200_1,plain,
! [A,B,C] :
( subset(relation_inverse_image(C,A),relation_inverse_image(C,B))
| ~ subset(A,B)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t178_relat_1]) ).
fof(f_200_2,plain,
! [U_790,U_789,U_788] :
( subset(relation_inverse_image(U_788,U_790),relation_inverse_image(U_788,U_789))
| ~ subset(U_790,U_789)
| ~ relation(U_788) ),
inference(variable_rename,[status(thm)],[f_200_1]) ).
cnf(f_200_3,plain,
( subset(relation_inverse_image(U_788,U_790),relation_inverse_image(U_788,U_789))
| ~ subset(U_790,U_789)
| ~ relation(U_788) ),
inference(clausify,[status(thm)],[f_200_2]) ).
fof(f_201_1,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(fof_nnf,[status(thm)],[t17_xboole_1]) ).
fof(f_201_2,plain,
! [U_792,U_791] : subset(set_intersection2(U_792,U_791),U_792),
inference(variable_rename,[status(thm)],[f_201_1]) ).
cnf(f_201_3,plain,
subset(set_intersection2(U_792,U_791),U_792),
inference(clausify,[status(thm)],[f_201_2]) ).
fof(f_202_1,plain,
! [A,B,C] :
( subset(A,set_intersection2(B,C))
| ~ subset(A,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t19_xboole_1]) ).
fof(f_202_2,plain,
! [U_795,U_794,U_793] :
( subset(U_795,set_intersection2(U_794,U_793))
| ~ subset(U_795,U_793)
| ~ subset(U_795,U_794) ),
inference(variable_rename,[status(thm)],[f_202_1]) ).
cnf(f_202_3,plain,
( subset(U_795,set_intersection2(U_794,U_793))
| ~ subset(U_795,U_793)
| ~ subset(U_795,U_794) ),
inference(clausify,[status(thm)],[f_202_2]) ).
fof(f_203_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_203_2,plain,
! [U_796] : set_union2(U_796,empty_set) = U_796,
inference(variable_rename,[status(thm)],[f_203_1]) ).
cnf(f_203_3,plain,
set_union2(U_796,empty_set) = U_796,
inference(clausify,[status(thm)],[f_203_2]) ).
fof(f_204_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_204_2,plain,
! [U_798,U_797] :
( element(U_798,U_797)
| ~ in(U_798,U_797) ),
inference(variable_rename,[status(thm)],[f_204_1]) ).
cnf(f_204_3,plain,
( element(U_798,U_797)
| ~ in(U_798,U_797) ),
inference(clausify,[status(thm)],[f_204_2]) ).
fof(f_205_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_205_2,plain,
! [U_801,U_800,U_799] :
( subset(U_801,U_799)
| ~ subset(U_800,U_799)
| ~ subset(U_801,U_800) ),
inference(variable_rename,[status(thm)],[f_205_1]) ).
cnf(f_205_3,plain,
( subset(U_801,U_799)
| ~ subset(U_800,U_799)
| ~ subset(U_801,U_800) ),
inference(clausify,[status(thm)],[f_205_2]) ).
fof(f_206_1,plain,
powerset(empty_set) = singleton(empty_set),
inference(fof_nnf,[status(thm)],[t1_zfmisc_1]) ).
cnf(f_206_2,plain,
powerset(empty_set) = singleton(empty_set),
inference(clausify,[status(thm)],[f_206_1]) ).
fof(f_207_1,plain,
! [A,B,C] :
( ( in(B,relation_rng(C))
& in(A,relation_dom(C)) )
| ~ in(ordered_pair(A,B),C)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t20_relat_1]) ).
fof(f_207_2,plain,
! [U_804,U_803,U_802] :
( ( in(U_803,relation_rng(U_802))
& in(U_804,relation_dom(U_802)) )
| ~ in(ordered_pair(U_804,U_803),U_802)
| ~ relation(U_802) ),
inference(variable_rename,[status(thm)],[f_207_1]) ).
cnf(f_207_3,plain,
( in(U_804,relation_dom(U_802))
| ~ in(ordered_pair(U_804,U_803),U_802)
| ~ relation(U_802) ),
inference(clausify,[status(thm)],[f_207_2]) ).
cnf(f_207_4,plain,
( in(U_803,relation_rng(U_802))
| ~ in(ordered_pair(U_804,U_803),U_802)
| ~ relation(U_802) ),
inference(clausify,[status(thm)],[f_207_2]) ).
fof(f_208_1,plain,
! [A,B] :
( ! [C] :
( ( ( in(A,relation_dom(relation_composition(C,B)))
| ~ in(apply(C,A),relation_dom(B))
| ~ in(A,relation_dom(C)) )
& ( ( in(apply(C,A),relation_dom(B))
& in(A,relation_dom(C)) )
| ~ in(A,relation_dom(relation_composition(C,B))) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t21_funct_1]) ).
fof(f_208_2,plain,
! [U_807,U_806] :
( ! [U_805] :
( ( ( in(U_807,relation_dom(relation_composition(U_805,U_806)))
| ~ in(apply(U_805,U_807),relation_dom(U_806))
| ~ in(U_807,relation_dom(U_805)) )
& ( ( in(apply(U_805,U_807),relation_dom(U_806))
& in(U_807,relation_dom(U_805)) )
| ~ in(U_807,relation_dom(relation_composition(U_805,U_806))) ) )
| ~ function(U_805)
| ~ relation(U_805) )
| ~ function(U_806)
| ~ relation(U_806) ),
inference(variable_rename,[status(thm)],[f_208_1]) ).
cnf(f_208_3,plain,
( in(U_807,relation_dom(U_805))
| ~ in(U_807,relation_dom(relation_composition(U_805,U_806)))
| ~ function(U_805)
| ~ relation(U_805)
| ~ function(U_806)
| ~ relation(U_806) ),
inference(clausify,[status(thm)],[f_208_2]) ).
cnf(f_208_4,plain,
( in(apply(U_805,U_807),relation_dom(U_806))
| ~ in(U_807,relation_dom(relation_composition(U_805,U_806)))
| ~ function(U_805)
| ~ relation(U_805)
| ~ function(U_806)
| ~ relation(U_806) ),
inference(clausify,[status(thm)],[f_208_2]) ).
cnf(f_208_5,plain,
( in(U_807,relation_dom(relation_composition(U_805,U_806)))
| ~ in(apply(U_805,U_807),relation_dom(U_806))
| ~ in(U_807,relation_dom(U_805))
| ~ function(U_805)
| ~ relation(U_805)
| ~ function(U_806)
| ~ relation(U_806) ),
inference(clausify,[status(thm)],[f_208_2]) ).
fof(f_209_1,plain,
! [A] :
( ! [B] :
( in(A,B)
| ~ proper_subset(A,B)
| ~ ordinal(B) )
| ~ epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[t21_ordinal1]) ).
fof(f_209_2,plain,
! [U_809] :
( ! [U_808] :
( in(U_809,U_808)
| ~ proper_subset(U_809,U_808)
| ~ ordinal(U_808) )
| ~ epsilon_transitive(U_809) ),
inference(variable_rename,[status(thm)],[f_209_1]) ).
cnf(f_209_3,plain,
( in(U_809,U_808)
| ~ proper_subset(U_809,U_808)
| ~ ordinal(U_808)
| ~ epsilon_transitive(U_809) ),
inference(clausify,[status(thm)],[f_209_2]) ).
fof(f_210_1,plain,
! [A] :
( subset(A,cartesian_product2(relation_dom(A),relation_rng(A)))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t21_relat_1]) ).
fof(f_210_2,plain,
! [U_810] :
( subset(U_810,cartesian_product2(relation_dom(U_810),relation_rng(U_810)))
| ~ relation(U_810) ),
inference(variable_rename,[status(thm)],[f_210_1]) ).
cnf(f_210_3,plain,
( subset(U_810,cartesian_product2(relation_dom(U_810),relation_rng(U_810)))
| ~ relation(U_810) ),
inference(clausify,[status(thm)],[f_210_2]) ).
fof(f_211_1,plain,
! [A,B] :
( ! [C] :
( apply(relation_composition(C,B),A) = apply(B,apply(C,A))
| ~ in(A,relation_dom(relation_composition(C,B)))
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t22_funct_1]) ).
fof(f_211_2,plain,
! [U_813,U_812] :
( ! [U_811] :
( apply(relation_composition(U_811,U_812),U_813) = apply(U_812,apply(U_811,U_813))
| ~ in(U_813,relation_dom(relation_composition(U_811,U_812)))
| ~ function(U_811)
| ~ relation(U_811) )
| ~ function(U_812)
| ~ relation(U_812) ),
inference(variable_rename,[status(thm)],[f_211_1]) ).
cnf(f_211_3,plain,
( apply(relation_composition(U_811,U_812),U_813) = apply(U_812,apply(U_811,U_813))
| ~ in(U_813,relation_dom(relation_composition(U_811,U_812)))
| ~ function(U_811)
| ~ relation(U_811)
| ~ function(U_812)
| ~ relation(U_812) ),
inference(clausify,[status(thm)],[f_211_2]) ).
fof(f_212_1,plain,
! [A,B] :
( ! [C] :
( apply(relation_composition(B,C),A) = apply(C,apply(B,A))
| ~ in(A,relation_dom(B))
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t23_funct_1]) ).
fof(f_212_2,plain,
! [U_816,U_815] :
( ! [U_814] :
( apply(relation_composition(U_815,U_814),U_816) = apply(U_814,apply(U_815,U_816))
| ~ in(U_816,relation_dom(U_815))
| ~ function(U_814)
| ~ relation(U_814) )
| ~ function(U_815)
| ~ relation(U_815) ),
inference(variable_rename,[status(thm)],[f_212_1]) ).
cnf(f_212_3,plain,
( apply(relation_composition(U_815,U_814),U_816) = apply(U_814,apply(U_815,U_816))
| ~ in(U_816,relation_dom(U_815))
| ~ function(U_814)
| ~ relation(U_814)
| ~ function(U_815)
| ~ relation(U_815) ),
inference(clausify,[status(thm)],[f_212_2]) ).
fof(f_213_1,plain,
! [A,B] :
( ordinal(A)
| ~ in(A,B)
| ~ ordinal(B) ),
inference(fof_nnf,[status(thm)],[t23_ordinal1]) ).
fof(f_213_2,plain,
! [U_818,U_817] :
( ordinal(U_818)
| ~ in(U_818,U_817)
| ~ ordinal(U_817) ),
inference(variable_rename,[status(thm)],[f_213_1]) ).
cnf(f_213_3,plain,
( ordinal(U_818)
| ~ in(U_818,U_817)
| ~ ordinal(U_817) ),
inference(clausify,[status(thm)],[f_213_2]) ).
fof(f_214_1,plain,
! [A] :
( ! [B] :
( in(B,A)
| A = B
| in(A,B)
| ~ ordinal(B) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t24_ordinal1]) ).
fof(f_214_2,plain,
! [U_820] :
( ! [U_819] :
( in(U_819,U_820)
| U_820 = U_819
| in(U_820,U_819)
| ~ ordinal(U_819) )
| ~ ordinal(U_820) ),
inference(variable_rename,[status(thm)],[f_214_1]) ).
cnf(f_214_3,plain,
( in(U_819,U_820)
| U_820 = U_819
| in(U_820,U_819)
| ~ ordinal(U_819)
| ~ ordinal(U_820) ),
inference(clausify,[status(thm)],[f_214_2]) ).
fof(f_215_1,plain,
! [A] :
( ! [B] :
( ( subset(relation_rng(A),relation_rng(B))
& subset(relation_dom(A),relation_dom(B)) )
| ~ subset(A,B)
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t25_relat_1]) ).
fof(f_215_2,plain,
! [U_822] :
( ! [U_821] :
( ( subset(relation_rng(U_822),relation_rng(U_821))
& subset(relation_dom(U_822),relation_dom(U_821)) )
| ~ subset(U_822,U_821)
| ~ relation(U_821) )
| ~ relation(U_822) ),
inference(variable_rename,[status(thm)],[f_215_1]) ).
cnf(f_215_3,plain,
( subset(relation_dom(U_822),relation_dom(U_821))
| ~ subset(U_822,U_821)
| ~ relation(U_821)
| ~ relation(U_822) ),
inference(clausify,[status(thm)],[f_215_2]) ).
cnf(f_215_4,plain,
( subset(relation_rng(U_822),relation_rng(U_821))
| ~ subset(U_822,U_821)
| ~ relation(U_821)
| ~ relation(U_822) ),
inference(clausify,[status(thm)],[f_215_2]) ).
fof(f_216_1,plain,
! [A,B,C] :
( subset(set_intersection2(A,C),set_intersection2(B,C))
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t26_xboole_1]) ).
fof(f_216_2,plain,
! [U_825,U_824,U_823] :
( subset(set_intersection2(U_825,U_823),set_intersection2(U_824,U_823))
| ~ subset(U_825,U_824) ),
inference(variable_rename,[status(thm)],[f_216_1]) ).
fof(f_216_3,plain,
! [U_825,U_824] :
( ! [U_823] : subset(set_intersection2(U_825,U_823),set_intersection2(U_824,U_823))
| ~ subset(U_825,U_824) ),
inference(miniscope,[status(thm)],[f_216_2]) ).
cnf(f_216_4,plain,
( subset(set_intersection2(U_825,U_823),set_intersection2(U_824,U_823))
| ~ subset(U_825,U_824) ),
inference(clausify,[status(thm)],[f_216_3]) ).
fof(f_217_1,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t28_xboole_1]) ).
fof(f_217_2,plain,
! [U_827,U_826] :
( set_intersection2(U_827,U_826) = U_827
| ~ subset(U_827,U_826) ),
inference(variable_rename,[status(thm)],[f_217_1]) ).
cnf(f_217_3,plain,
( set_intersection2(U_827,U_826) = U_827
| ~ subset(U_827,U_826) ),
inference(clausify,[status(thm)],[f_217_2]) ).
fof(f_218_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_218_2,plain,
! [U_828] : set_intersection2(U_828,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_218_1]) ).
cnf(f_218_3,plain,
set_intersection2(U_828,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_218_2]) ).
fof(f_219_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_219_2,plain,
! [U_830,U_829] :
( in(U_830,U_829)
| empty(U_829)
| ~ element(U_830,U_829) ),
inference(variable_rename,[status(thm)],[f_219_1]) ).
cnf(f_219_3,plain,
( in(U_830,U_829)
| empty(U_829)
| ~ element(U_830,U_829) ),
inference(clausify,[status(thm)],[f_219_2]) ).
fof(f_220_1,plain,
! [A,B] :
( A = B
| ? [C] :
( ( ~ in(C,A)
& in(C,B) )
| ( ~ in(C,B)
& in(C,A) ) ) ),
inference(fof_nnf,[status(thm)],[t2_tarski]) ).
fof(f_220_2,plain,
! [U_833,U_832] :
( U_833 = U_832
| ? [U_831] :
( ( ~ in(U_831,U_833)
& in(U_831,U_832) )
| ( ~ in(U_831,U_832)
& in(U_831,U_833) ) ) ),
inference(variable_rename,[status(thm)],[f_220_1]) ).
fof(f_220_3,plain,
! [U_833,U_832] :
( U_833 = U_832
| ? [U_835] :
( ~ in(U_835,U_833)
& in(U_835,U_832) )
| ? [U_834] :
( ~ in(U_834,U_832)
& in(U_834,U_833) ) ),
inference(miniscope,[status(thm)],[f_220_2]) ).
fof(f_220_4,plain,
! [U_833,U_832] :
( U_833 = U_832
| ? [U_835] :
( ~ in(U_835,U_833)
& in(U_835,U_832) )
| ( ~ in(sK133(U_833,U_832),U_832)
& in(sK133(U_833,U_832),U_833) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK133]),skolemize(U_834,sK133(U_833,U_832))],[f_220_3]) ).
fof(f_220_5,plain,
! [U_833,U_832] :
( U_833 = U_832
| ( ~ in(sK134(U_833,U_832),U_833)
& in(sK134(U_833,U_832),U_832) )
| ( ~ in(sK133(U_833,U_832),U_832)
& in(sK133(U_833,U_832),U_833) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK134]),skolemize(U_835,sK134(U_833,U_832))],[f_220_4]) ).
cnf(f_220_6,plain,
( in(sK134(U_833,U_832),U_832)
| in(sK133(U_833,U_832),U_833)
| U_833 = U_832 ),
inference(clausify,[status(thm)],[f_220_5]) ).
cnf(f_220_7,plain,
( ~ in(sK134(U_833,U_832),U_833)
| in(sK133(U_833,U_832),U_833)
| U_833 = U_832 ),
inference(clausify,[status(thm)],[f_220_5]) ).
cnf(f_220_8,plain,
( in(sK134(U_833,U_832),U_832)
| ~ in(sK133(U_833,U_832),U_832)
| U_833 = U_832 ),
inference(clausify,[status(thm)],[f_220_5]) ).
cnf(f_220_9,plain,
( ~ in(sK134(U_833,U_832),U_833)
| ~ in(sK133(U_833,U_832),U_832)
| U_833 = U_832 ),
inference(clausify,[status(thm)],[f_220_5]) ).
fof(f_221_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_221_2,plain,
! [U_836] : subset(empty_set,U_836),
inference(variable_rename,[status(thm)],[f_221_1]) ).
cnf(f_221_3,plain,
subset(empty_set,U_836),
inference(clausify,[status(thm)],[f_221_2]) ).
fof(f_222_1,plain,
! [A,B,C] :
( ( in(B,relation_field(C))
& in(A,relation_field(C)) )
| ~ in(ordered_pair(A,B),C)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t30_relat_1]) ).
fof(f_222_2,plain,
! [U_839,U_838,U_837] :
( ( in(U_838,relation_field(U_837))
& in(U_839,relation_field(U_837)) )
| ~ in(ordered_pair(U_839,U_838),U_837)
| ~ relation(U_837) ),
inference(variable_rename,[status(thm)],[f_222_1]) ).
cnf(f_222_3,plain,
( in(U_839,relation_field(U_837))
| ~ in(ordered_pair(U_839,U_838),U_837)
| ~ relation(U_837) ),
inference(clausify,[status(thm)],[f_222_2]) ).
cnf(f_222_4,plain,
( in(U_838,relation_field(U_837))
| ~ in(ordered_pair(U_839,U_838),U_837)
| ~ relation(U_837) ),
inference(clausify,[status(thm)],[f_222_2]) ).
fof(f_223_1,plain,
! [A] :
( ordinal(A)
| ? [B] :
( ( ~ subset(B,A)
| ~ ordinal(B) )
& in(B,A) ) ),
inference(fof_nnf,[status(thm)],[t31_ordinal1]) ).
fof(f_223_2,plain,
! [U_841] :
( ordinal(U_841)
| ? [U_840] :
( ( ~ subset(U_840,U_841)
| ~ ordinal(U_840) )
& in(U_840,U_841) ) ),
inference(variable_rename,[status(thm)],[f_223_1]) ).
fof(f_223_3,plain,
! [U_841] :
( ordinal(U_841)
| ( ( ~ subset(sK135(U_841),U_841)
| ~ ordinal(sK135(U_841)) )
& in(sK135(U_841),U_841) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK135]),skolemize(U_840,sK135(U_841))],[f_223_2]) ).
cnf(f_223_4,plain,
( in(sK135(U_841),U_841)
| ordinal(U_841) ),
inference(clausify,[status(thm)],[f_223_3]) ).
cnf(f_223_5,plain,
( ~ subset(sK135(U_841),U_841)
| ~ ordinal(sK135(U_841))
| ordinal(U_841) ),
inference(clausify,[status(thm)],[f_223_3]) ).
fof(f_224_1,plain,
! [A,B] :
( ? [C] :
( ! [D] :
( ordinal_subset(C,D)
| ~ in(D,A)
| ~ ordinal(D) )
& in(C,A)
& ordinal(C) )
| A = empty_set
| ~ subset(A,B)
| ~ ordinal(B) ),
inference(fof_nnf,[status(thm)],[t32_ordinal1]) ).
fof(f_224_2,plain,
! [U_845,U_844] :
( ? [U_843] :
( ! [U_842] :
( ordinal_subset(U_843,U_842)
| ~ in(U_842,U_845)
| ~ ordinal(U_842) )
& in(U_843,U_845)
& ordinal(U_843) )
| U_845 = empty_set
| ~ subset(U_845,U_844)
| ~ ordinal(U_844) ),
inference(variable_rename,[status(thm)],[f_224_1]) ).
fof(f_224_3,plain,
! [U_845,U_844] :
( ( ! [U_842] :
( ordinal_subset(sK136(U_845,U_844),U_842)
| ~ in(U_842,U_845)
| ~ ordinal(U_842) )
& in(sK136(U_845,U_844),U_845)
& ordinal(sK136(U_845,U_844)) )
| U_845 = empty_set
| ~ subset(U_845,U_844)
| ~ ordinal(U_844) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK136]),skolemize(U_843,sK136(U_845,U_844))],[f_224_2]) ).
cnf(f_224_4,plain,
( ordinal(sK136(U_845,U_844))
| U_845 = empty_set
| ~ subset(U_845,U_844)
| ~ ordinal(U_844) ),
inference(clausify,[status(thm)],[f_224_3]) ).
cnf(f_224_5,plain,
( in(sK136(U_845,U_844),U_845)
| U_845 = empty_set
| ~ subset(U_845,U_844)
| ~ ordinal(U_844) ),
inference(clausify,[status(thm)],[f_224_3]) ).
cnf(f_224_6,plain,
( ordinal_subset(sK136(U_845,U_844),U_842)
| ~ in(U_842,U_845)
| ~ ordinal(U_842)
| U_845 = empty_set
| ~ subset(U_845,U_844)
| ~ ordinal(U_844) ),
inference(clausify,[status(thm)],[f_224_3]) ).
fof(f_225_1,plain,
! [A] :
( ! [B] :
( ( ( in(A,B)
| ~ ordinal_subset(succ(A),B) )
& ( ordinal_subset(succ(A),B)
| ~ in(A,B) ) )
| ~ ordinal(B) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t33_ordinal1]) ).
fof(f_225_2,plain,
! [U_847] :
( ! [U_846] :
( ( ( in(U_847,U_846)
| ~ ordinal_subset(succ(U_847),U_846) )
& ( ordinal_subset(succ(U_847),U_846)
| ~ in(U_847,U_846) ) )
| ~ ordinal(U_846) )
| ~ ordinal(U_847) ),
inference(variable_rename,[status(thm)],[f_225_1]) ).
cnf(f_225_3,plain,
( ordinal_subset(succ(U_847),U_846)
| ~ in(U_847,U_846)
| ~ ordinal(U_846)
| ~ ordinal(U_847) ),
inference(clausify,[status(thm)],[f_225_2]) ).
cnf(f_225_4,plain,
( in(U_847,U_846)
| ~ ordinal_subset(succ(U_847),U_846)
| ~ ordinal(U_846)
| ~ ordinal(U_847) ),
inference(clausify,[status(thm)],[f_225_2]) ).
fof(f_226_1,plain,
! [A,B,C] :
( subset(set_difference(A,C),set_difference(B,C))
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t33_xboole_1]) ).
fof(f_226_2,plain,
! [U_850,U_849,U_848] :
( subset(set_difference(U_850,U_848),set_difference(U_849,U_848))
| ~ subset(U_850,U_849) ),
inference(variable_rename,[status(thm)],[f_226_1]) ).
fof(f_226_3,plain,
! [U_850,U_849] :
( ! [U_848] : subset(set_difference(U_850,U_848),set_difference(U_849,U_848))
| ~ subset(U_850,U_849) ),
inference(miniscope,[status(thm)],[f_226_2]) ).
cnf(f_226_4,plain,
( subset(set_difference(U_850,U_848),set_difference(U_849,U_848))
| ~ subset(U_850,U_849) ),
inference(clausify,[status(thm)],[f_226_3]) ).
fof(f_227_1,plain,
! [A,B,C,D] :
( ( B = D
& A = C )
| ordered_pair(A,B) != ordered_pair(C,D) ),
inference(fof_nnf,[status(thm)],[t33_zfmisc_1]) ).
fof(f_227_2,plain,
! [U_854,U_853,U_852,U_851] :
( ( U_853 = U_851
& U_854 = U_852 )
| ordered_pair(U_854,U_853) != ordered_pair(U_852,U_851) ),
inference(variable_rename,[status(thm)],[f_227_1]) ).
cnf(f_227_3,plain,
( U_854 = U_852
| ordered_pair(U_854,U_853) != ordered_pair(U_852,U_851) ),
inference(clausify,[status(thm)],[f_227_2]) ).
cnf(f_227_4,plain,
( U_853 = U_851
| ordered_pair(U_854,U_853) != ordered_pair(U_852,U_851) ),
inference(clausify,[status(thm)],[f_227_2]) ).
fof(f_228_1,plain,
! [A,B] :
( ( ( B = identity_relation(A)
| ? [C] :
( apply(B,C) != C
& in(C,A) )
| relation_dom(B) != A )
& ( ( ! [C] :
( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A )
| B != identity_relation(A) ) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t34_funct_1]) ).
fof(f_228_2,plain,
! [U_858,U_857] :
( ( ( U_857 = identity_relation(U_858)
| ? [U_856] :
( apply(U_857,U_856) != U_856
& in(U_856,U_858) )
| relation_dom(U_857) != U_858 )
& ( ( ! [U_855] :
( apply(U_857,U_855) = U_855
| ~ in(U_855,U_858) )
& relation_dom(U_857) = U_858 )
| U_857 != identity_relation(U_858) ) )
| ~ function(U_857)
| ~ relation(U_857) ),
inference(variable_rename,[status(thm)],[f_228_1]) ).
fof(f_228_3,plain,
! [U_858,U_857] :
( ( ( U_857 = identity_relation(U_858)
| ( apply(U_857,sK137(U_858,U_857)) != sK137(U_858,U_857)
& in(sK137(U_858,U_857),U_858) )
| relation_dom(U_857) != U_858 )
& ( ( ! [U_855] :
( apply(U_857,U_855) = U_855
| ~ in(U_855,U_858) )
& relation_dom(U_857) = U_858 )
| U_857 != identity_relation(U_858) ) )
| ~ function(U_857)
| ~ relation(U_857) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK137]),skolemize(U_856,sK137(U_858,U_857))],[f_228_2]) ).
cnf(f_228_4,plain,
( relation_dom(U_857) = U_858
| U_857 != identity_relation(U_858)
| ~ function(U_857)
| ~ relation(U_857) ),
inference(clausify,[status(thm)],[f_228_3]) ).
cnf(f_228_5,plain,
( apply(U_857,U_855) = U_855
| ~ in(U_855,U_858)
| U_857 != identity_relation(U_858)
| ~ function(U_857)
| ~ relation(U_857) ),
inference(clausify,[status(thm)],[f_228_3]) ).
cnf(f_228_6,plain,
( in(sK137(U_858,U_857),U_858)
| relation_dom(U_857) != U_858
| U_857 = identity_relation(U_858)
| ~ function(U_857)
| ~ relation(U_857) ),
inference(clausify,[status(thm)],[f_228_3]) ).
cnf(f_228_7,plain,
( apply(U_857,sK137(U_858,U_857)) != sK137(U_858,U_857)
| relation_dom(U_857) != U_858
| U_857 = identity_relation(U_858)
| ~ function(U_857)
| ~ relation(U_857) ),
inference(clausify,[status(thm)],[f_228_3]) ).
fof(f_229_1,plain,
! [A,B] :
( apply(identity_relation(A),B) = B
| ~ in(B,A) ),
inference(fof_nnf,[status(thm)],[t35_funct_1]) ).
fof(f_229_2,plain,
! [U_860,U_859] :
( apply(identity_relation(U_860),U_859) = U_859
| ~ in(U_859,U_860) ),
inference(variable_rename,[status(thm)],[f_229_1]) ).
cnf(f_229_3,plain,
( apply(identity_relation(U_860),U_859) = U_859
| ~ in(U_859,U_860) ),
inference(clausify,[status(thm)],[f_229_2]) ).
fof(f_230_1,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(fof_nnf,[status(thm)],[t36_xboole_1]) ).
fof(f_230_2,plain,
! [U_862,U_861] : subset(set_difference(U_862,U_861),U_862),
inference(variable_rename,[status(thm)],[f_230_1]) ).
cnf(f_230_3,plain,
subset(set_difference(U_862,U_861),U_862),
inference(clausify,[status(thm)],[f_230_2]) ).
fof(f_231_1,plain,
! [A] :
( ( relation_dom(A) = relation_rng(relation_inverse(A))
& relation_rng(A) = relation_dom(relation_inverse(A)) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t37_relat_1]) ).
fof(f_231_2,plain,
! [U_863] :
( ( relation_dom(U_863) = relation_rng(relation_inverse(U_863))
& relation_rng(U_863) = relation_dom(relation_inverse(U_863)) )
| ~ relation(U_863) ),
inference(variable_rename,[status(thm)],[f_231_1]) ).
cnf(f_231_3,plain,
( relation_rng(U_863) = relation_dom(relation_inverse(U_863))
| ~ relation(U_863) ),
inference(clausify,[status(thm)],[f_231_2]) ).
cnf(f_231_4,plain,
( relation_dom(U_863) = relation_rng(relation_inverse(U_863))
| ~ relation(U_863) ),
inference(clausify,[status(thm)],[f_231_2]) ).
fof(f_232_1,plain,
! [A,B] :
( ( set_difference(A,B) = empty_set
| ~ subset(A,B) )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(fof_nnf,[status(thm)],[t37_xboole_1]) ).
fof(f_232_2,plain,
! [U_865,U_864] :
( ( set_difference(U_865,U_864) = empty_set
| ~ subset(U_865,U_864) )
& ( subset(U_865,U_864)
| set_difference(U_865,U_864) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_232_1]) ).
fof(f_232_3,plain,
( ! [U_869,U_867] :
( set_difference(U_869,U_867) = empty_set
| ~ subset(U_869,U_867) )
& ! [U_868,U_866] :
( subset(U_868,U_866)
| set_difference(U_868,U_866) != empty_set ) ),
inference(miniscope,[status(thm)],[f_232_2]) ).
cnf(f_232_4,plain,
( subset(U_868,U_866)
| set_difference(U_868,U_866) != empty_set ),
inference(clausify,[status(thm)],[f_232_3]) ).
cnf(f_232_5,plain,
( set_difference(U_869,U_867) = empty_set
| ~ subset(U_869,U_867) ),
inference(clausify,[status(thm)],[f_232_3]) ).
fof(f_233_1,plain,
! [A,B] :
( ( subset(singleton(A),B)
| ~ in(A,B) )
& ( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(fof_nnf,[status(thm)],[t37_zfmisc_1]) ).
fof(f_233_2,plain,
! [U_871,U_870] :
( ( subset(singleton(U_871),U_870)
| ~ in(U_871,U_870) )
& ( in(U_871,U_870)
| ~ subset(singleton(U_871),U_870) ) ),
inference(variable_rename,[status(thm)],[f_233_1]) ).
fof(f_233_3,plain,
( ! [U_875,U_873] :
( subset(singleton(U_875),U_873)
| ~ in(U_875,U_873) )
& ! [U_874,U_872] :
( in(U_874,U_872)
| ~ subset(singleton(U_874),U_872) ) ),
inference(miniscope,[status(thm)],[f_233_2]) ).
cnf(f_233_4,plain,
( in(U_874,U_872)
| ~ subset(singleton(U_874),U_872) ),
inference(clausify,[status(thm)],[f_233_3]) ).
cnf(f_233_5,plain,
( subset(singleton(U_875),U_873)
| ~ in(U_875,U_873) ),
inference(clausify,[status(thm)],[f_233_3]) ).
fof(f_234_1,plain,
! [A,B,C] :
( ( subset(unordered_pair(A,B),C)
| ~ in(B,C)
| ~ in(A,C) )
& ( ( in(B,C)
& in(A,C) )
| ~ subset(unordered_pair(A,B),C) ) ),
inference(fof_nnf,[status(thm)],[t38_zfmisc_1]) ).
fof(f_234_2,plain,
! [U_878,U_877,U_876] :
( ( subset(unordered_pair(U_878,U_877),U_876)
| ~ in(U_877,U_876)
| ~ in(U_878,U_876) )
& ( ( in(U_877,U_876)
& in(U_878,U_876) )
| ~ subset(unordered_pair(U_878,U_877),U_876) ) ),
inference(variable_rename,[status(thm)],[f_234_1]) ).
fof(f_234_3,plain,
( ! [U_884,U_882,U_880] :
( subset(unordered_pair(U_884,U_882),U_880)
| ~ in(U_882,U_880)
| ~ in(U_884,U_880) )
& ! [U_883,U_881,U_879] :
( ( in(U_881,U_879)
& in(U_883,U_879) )
| ~ subset(unordered_pair(U_883,U_881),U_879) ) ),
inference(miniscope,[status(thm)],[f_234_2]) ).
cnf(f_234_4,plain,
( in(U_883,U_879)
| ~ subset(unordered_pair(U_883,U_881),U_879) ),
inference(clausify,[status(thm)],[f_234_3]) ).
cnf(f_234_5,plain,
( in(U_881,U_879)
| ~ subset(unordered_pair(U_883,U_881),U_879) ),
inference(clausify,[status(thm)],[f_234_3]) ).
cnf(f_234_6,plain,
( subset(unordered_pair(U_884,U_882),U_880)
| ~ in(U_882,U_880)
| ~ in(U_884,U_880) ),
inference(clausify,[status(thm)],[f_234_3]) ).
fof(f_235_1,plain,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(fof_nnf,[status(thm)],[t39_xboole_1]) ).
fof(f_235_2,plain,
! [U_886,U_885] : set_union2(U_886,set_difference(U_885,U_886)) = set_union2(U_886,U_885),
inference(variable_rename,[status(thm)],[f_235_1]) ).
cnf(f_235_3,plain,
set_union2(U_886,set_difference(U_885,U_886)) = set_union2(U_886,U_885),
inference(clausify,[status(thm)],[f_235_2]) ).
fof(f_236_1,plain,
! [A,B] :
( ( subset(A,singleton(B))
| ( A != singleton(B)
& A != empty_set ) )
& ( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(fof_nnf,[status(thm)],[t39_zfmisc_1]) ).
fof(f_236_2,plain,
! [U_888,U_887] :
( ( subset(U_888,singleton(U_887))
| ( U_888 != singleton(U_887)
& U_888 != empty_set ) )
& ( U_888 = singleton(U_887)
| U_888 = empty_set
| ~ subset(U_888,singleton(U_887)) ) ),
inference(variable_rename,[status(thm)],[f_236_1]) ).
fof(f_236_3,plain,
( ! [U_892,U_890] :
( subset(U_892,singleton(U_890))
| ( U_892 != singleton(U_890)
& U_892 != empty_set ) )
& ! [U_891,U_889] :
( U_891 = singleton(U_889)
| U_891 = empty_set
| ~ subset(U_891,singleton(U_889)) ) ),
inference(miniscope,[status(thm)],[f_236_2]) ).
cnf(f_236_4,plain,
( U_891 = singleton(U_889)
| U_891 = empty_set
| ~ subset(U_891,singleton(U_889)) ),
inference(clausify,[status(thm)],[f_236_3]) ).
cnf(f_236_5,plain,
( U_892 != empty_set
| subset(U_892,singleton(U_890)) ),
inference(clausify,[status(thm)],[f_236_3]) ).
cnf(f_236_6,plain,
( U_892 != singleton(U_890)
| subset(U_892,singleton(U_890)) ),
inference(clausify,[status(thm)],[f_236_3]) ).
fof(f_237_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_237_2,plain,
! [U_893] : set_difference(U_893,empty_set) = U_893,
inference(variable_rename,[status(thm)],[f_237_1]) ).
cnf(f_237_3,plain,
set_difference(U_893,empty_set) = U_893,
inference(clausify,[status(thm)],[f_237_2]) ).
fof(f_238_1,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ in(B,C)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t3_ordinal1]) ).
fof(f_238_2,plain,
! [U_896,U_895,U_894] :
( ~ in(U_894,U_896)
| ~ in(U_895,U_894)
| ~ in(U_896,U_895) ),
inference(variable_rename,[status(thm)],[f_238_1]) ).
fof(f_238_3,plain,
! [U_896,U_895] :
( ! [U_894] :
( ~ in(U_894,U_896)
| ~ in(U_895,U_894) )
| ~ in(U_896,U_895) ),
inference(miniscope,[status(thm)],[f_238_2]) ).
cnf(f_238_4,plain,
( ~ in(U_894,U_896)
| ~ in(U_895,U_894)
| ~ in(U_896,U_895) ),
inference(clausify,[status(thm)],[f_238_3]) ).
fof(f_239_1,plain,
! [A,B] :
( ( element(A,powerset(B))
| ~ subset(A,B) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(fof_nnf,[status(thm)],[t3_subset]) ).
fof(f_239_2,plain,
! [U_898,U_897] :
( ( element(U_898,powerset(U_897))
| ~ subset(U_898,U_897) )
& ( subset(U_898,U_897)
| ~ element(U_898,powerset(U_897)) ) ),
inference(variable_rename,[status(thm)],[f_239_1]) ).
fof(f_239_3,plain,
( ! [U_902,U_900] :
( element(U_902,powerset(U_900))
| ~ subset(U_902,U_900) )
& ! [U_901,U_899] :
( subset(U_901,U_899)
| ~ element(U_901,powerset(U_899)) ) ),
inference(miniscope,[status(thm)],[f_239_2]) ).
cnf(f_239_4,plain,
( subset(U_901,U_899)
| ~ element(U_901,powerset(U_899)) ),
inference(clausify,[status(thm)],[f_239_3]) ).
cnf(f_239_5,plain,
( element(U_902,powerset(U_900))
| ~ subset(U_902,U_900) ),
inference(clausify,[status(thm)],[f_239_3]) ).
fof(f_240_1,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] :
( ~ in(C,B)
| ~ in(C,A) ) )
& ( ? [C] :
( in(C,B)
& in(C,A) )
| disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t3_xboole_0]) ).
fof(f_240_2,plain,
! [U_906,U_905] :
( ( ~ disjoint(U_906,U_905)
| ! [U_904] :
( ~ in(U_904,U_905)
| ~ in(U_904,U_906) ) )
& ( ? [U_903] :
( in(U_903,U_905)
& in(U_903,U_906) )
| disjoint(U_906,U_905) ) ),
inference(variable_rename,[status(thm)],[f_240_1]) ).
fof(f_240_3,plain,
( ! [U_910,U_908] :
( ~ disjoint(U_910,U_908)
| ! [U_904] :
( ~ in(U_904,U_908)
| ~ in(U_904,U_910) ) )
& ! [U_909,U_907] :
( ? [U_903] :
( in(U_903,U_907)
& in(U_903,U_909) )
| disjoint(U_909,U_907) ) ),
inference(miniscope,[status(thm)],[f_240_2]) ).
fof(f_240_4,plain,
( ! [U_910,U_908] :
( ~ disjoint(U_910,U_908)
| ! [U_904] :
( ~ in(U_904,U_908)
| ~ in(U_904,U_910) ) )
& ! [U_909,U_907] :
( ( in(sK138(U_909,U_907),U_907)
& in(sK138(U_909,U_907),U_909) )
| disjoint(U_909,U_907) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK138]),skolemize(U_903,sK138(U_909,U_907))],[f_240_3]) ).
cnf(f_240_5,plain,
( in(sK138(U_909,U_907),U_909)
| disjoint(U_909,U_907) ),
inference(clausify,[status(thm)],[f_240_4]) ).
cnf(f_240_6,plain,
( in(sK138(U_909,U_907),U_907)
| disjoint(U_909,U_907) ),
inference(clausify,[status(thm)],[f_240_4]) ).
cnf(f_240_7,plain,
( ~ disjoint(U_910,U_908)
| ~ in(U_904,U_908)
| ~ in(U_904,U_910) ),
inference(clausify,[status(thm)],[f_240_4]) ).
fof(f_241_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_241_2,plain,
! [U_911] :
( U_911 = empty_set
| ~ subset(U_911,empty_set) ),
inference(variable_rename,[status(thm)],[f_241_1]) ).
cnf(f_241_3,plain,
( U_911 = empty_set
| ~ subset(U_911,empty_set) ),
inference(clausify,[status(thm)],[f_241_2]) ).
fof(f_242_1,plain,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(fof_nnf,[status(thm)],[t40_xboole_1]) ).
fof(f_242_2,plain,
! [U_913,U_912] : set_difference(set_union2(U_913,U_912),U_912) = set_difference(U_913,U_912),
inference(variable_rename,[status(thm)],[f_242_1]) ).
cnf(f_242_3,plain,
set_difference(set_union2(U_913,U_912),U_912) = set_difference(U_913,U_912),
inference(clausify,[status(thm)],[f_242_2]) ).
fof(f_243_1,plain,
! [A] :
( ( ( being_limit_ordinal(A)
| ? [B] :
( ~ in(succ(B),A)
& in(B,A)
& ordinal(B) ) )
& ( ! [B] :
( in(succ(B),A)
| ~ in(B,A)
| ~ ordinal(B) )
| ~ being_limit_ordinal(A) ) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t41_ordinal1]) ).
fof(f_243_2,plain,
! [U_916] :
( ( ( being_limit_ordinal(U_916)
| ? [U_915] :
( ~ in(succ(U_915),U_916)
& in(U_915,U_916)
& ordinal(U_915) ) )
& ( ! [U_914] :
( in(succ(U_914),U_916)
| ~ in(U_914,U_916)
| ~ ordinal(U_914) )
| ~ being_limit_ordinal(U_916) ) )
| ~ ordinal(U_916) ),
inference(variable_rename,[status(thm)],[f_243_1]) ).
fof(f_243_3,plain,
! [U_916] :
( ( ( being_limit_ordinal(U_916)
| ( ~ in(succ(sK139(U_916)),U_916)
& in(sK139(U_916),U_916)
& ordinal(sK139(U_916)) ) )
& ( ! [U_914] :
( in(succ(U_914),U_916)
| ~ in(U_914,U_916)
| ~ ordinal(U_914) )
| ~ being_limit_ordinal(U_916) ) )
| ~ ordinal(U_916) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK139]),skolemize(U_915,sK139(U_916))],[f_243_2]) ).
cnf(f_243_4,plain,
( in(succ(U_914),U_916)
| ~ in(U_914,U_916)
| ~ ordinal(U_914)
| ~ being_limit_ordinal(U_916)
| ~ ordinal(U_916) ),
inference(clausify,[status(thm)],[f_243_3]) ).
cnf(f_243_5,plain,
( ordinal(sK139(U_916))
| being_limit_ordinal(U_916)
| ~ ordinal(U_916) ),
inference(clausify,[status(thm)],[f_243_3]) ).
cnf(f_243_6,plain,
( in(sK139(U_916),U_916)
| being_limit_ordinal(U_916)
| ~ ordinal(U_916) ),
inference(clausify,[status(thm)],[f_243_3]) ).
cnf(f_243_7,plain,
( ~ in(succ(sK139(U_916)),U_916)
| being_limit_ordinal(U_916)
| ~ ordinal(U_916) ),
inference(clausify,[status(thm)],[f_243_3]) ).
fof(f_244_1,plain,
! [A] :
( ( ( ~ being_limit_ordinal(A)
| ! [B] :
( A != succ(B)
| ~ ordinal(B) ) )
& ( ? [B] :
( A = succ(B)
& ordinal(B) )
| being_limit_ordinal(A) ) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t42_ordinal1]) ).
fof(f_244_2,plain,
! [U_919] :
( ( ( ~ being_limit_ordinal(U_919)
| ! [U_918] :
( U_919 != succ(U_918)
| ~ ordinal(U_918) ) )
& ( ? [U_917] :
( U_919 = succ(U_917)
& ordinal(U_917) )
| being_limit_ordinal(U_919) ) )
| ~ ordinal(U_919) ),
inference(variable_rename,[status(thm)],[f_244_1]) ).
fof(f_244_3,plain,
! [U_919] :
( ( ( ~ being_limit_ordinal(U_919)
| ! [U_918] :
( U_919 != succ(U_918)
| ~ ordinal(U_918) ) )
& ( ( U_919 = succ(sK140(U_919))
& ordinal(sK140(U_919)) )
| being_limit_ordinal(U_919) ) )
| ~ ordinal(U_919) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK140]),skolemize(U_917,sK140(U_919))],[f_244_2]) ).
cnf(f_244_4,plain,
( ordinal(sK140(U_919))
| being_limit_ordinal(U_919)
| ~ ordinal(U_919) ),
inference(clausify,[status(thm)],[f_244_3]) ).
cnf(f_244_5,plain,
( U_919 = succ(sK140(U_919))
| being_limit_ordinal(U_919)
| ~ ordinal(U_919) ),
inference(clausify,[status(thm)],[f_244_3]) ).
cnf(f_244_6,plain,
( ~ being_limit_ordinal(U_919)
| U_919 != succ(U_918)
| ~ ordinal(U_918)
| ~ ordinal(U_919) ),
inference(clausify,[status(thm)],[f_244_3]) ).
fof(f_245_1,plain,
! [A,B] :
( ! [C] :
( ( ( disjoint(B,C)
| ~ subset(B,subset_complement(A,C)) )
& ( subset(B,subset_complement(A,C))
| ~ disjoint(B,C) ) )
| ~ element(C,powerset(A)) )
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[t43_subset_1]) ).
fof(f_245_2,plain,
! [U_922,U_921] :
( ! [U_920] :
( ( ( disjoint(U_921,U_920)
| ~ subset(U_921,subset_complement(U_922,U_920)) )
& ( subset(U_921,subset_complement(U_922,U_920))
| ~ disjoint(U_921,U_920) ) )
| ~ element(U_920,powerset(U_922)) )
| ~ element(U_921,powerset(U_922)) ),
inference(variable_rename,[status(thm)],[f_245_1]) ).
cnf(f_245_3,plain,
( subset(U_921,subset_complement(U_922,U_920))
| ~ disjoint(U_921,U_920)
| ~ element(U_920,powerset(U_922))
| ~ element(U_921,powerset(U_922)) ),
inference(clausify,[status(thm)],[f_245_2]) ).
cnf(f_245_4,plain,
( disjoint(U_921,U_920)
| ~ subset(U_921,subset_complement(U_922,U_920))
| ~ element(U_920,powerset(U_922))
| ~ element(U_921,powerset(U_922)) ),
inference(clausify,[status(thm)],[f_245_2]) ).
fof(f_246_1,plain,
! [A] :
( ! [B] :
( subset(relation_dom(relation_composition(A,B)),relation_dom(A))
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t44_relat_1]) ).
fof(f_246_2,plain,
! [U_924] :
( ! [U_923] :
( subset(relation_dom(relation_composition(U_924,U_923)),relation_dom(U_924))
| ~ relation(U_923) )
| ~ relation(U_924) ),
inference(variable_rename,[status(thm)],[f_246_1]) ).
cnf(f_246_3,plain,
( subset(relation_dom(relation_composition(U_924,U_923)),relation_dom(U_924))
| ~ relation(U_923)
| ~ relation(U_924) ),
inference(clausify,[status(thm)],[f_246_2]) ).
fof(f_247_1,plain,
! [A] :
( ! [B] :
( subset(relation_rng(relation_composition(A,B)),relation_rng(B))
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t45_relat_1]) ).
fof(f_247_2,plain,
! [U_926] :
( ! [U_925] :
( subset(relation_rng(relation_composition(U_926,U_925)),relation_rng(U_925))
| ~ relation(U_925) )
| ~ relation(U_926) ),
inference(variable_rename,[status(thm)],[f_247_1]) ).
cnf(f_247_3,plain,
( subset(relation_rng(relation_composition(U_926,U_925)),relation_rng(U_925))
| ~ relation(U_925)
| ~ relation(U_926) ),
inference(clausify,[status(thm)],[f_247_2]) ).
fof(f_248_1,plain,
! [A,B] :
( B = set_union2(A,set_difference(B,A))
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t45_xboole_1]) ).
fof(f_248_2,plain,
! [U_928,U_927] :
( U_927 = set_union2(U_928,set_difference(U_927,U_928))
| ~ subset(U_928,U_927) ),
inference(variable_rename,[status(thm)],[f_248_1]) ).
cnf(f_248_3,plain,
( U_927 = set_union2(U_928,set_difference(U_927,U_928))
| ~ subset(U_928,U_927) ),
inference(clausify,[status(thm)],[f_248_2]) ).
fof(f_249_1,plain,
! [A] :
( ! [B] :
( relation_dom(relation_composition(A,B)) = relation_dom(A)
| ~ subset(relation_rng(A),relation_dom(B))
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t46_relat_1]) ).
fof(f_249_2,plain,
! [U_930] :
( ! [U_929] :
( relation_dom(relation_composition(U_930,U_929)) = relation_dom(U_930)
| ~ subset(relation_rng(U_930),relation_dom(U_929))
| ~ relation(U_929) )
| ~ relation(U_930) ),
inference(variable_rename,[status(thm)],[f_249_1]) ).
cnf(f_249_3,plain,
( relation_dom(relation_composition(U_930,U_929)) = relation_dom(U_930)
| ~ subset(relation_rng(U_930),relation_dom(U_929))
| ~ relation(U_929)
| ~ relation(U_930) ),
inference(clausify,[status(thm)],[f_249_2]) ).
fof(f_250_1,plain,
! [A,B] :
( complements_of_subsets(A,B) != empty_set
| B = empty_set
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[t46_setfam_1]) ).
fof(f_250_2,plain,
! [U_932,U_931] :
( complements_of_subsets(U_932,U_931) != empty_set
| U_931 = empty_set
| ~ element(U_931,powerset(powerset(U_932))) ),
inference(variable_rename,[status(thm)],[f_250_1]) ).
cnf(f_250_3,plain,
( complements_of_subsets(U_932,U_931) != empty_set
| U_931 = empty_set
| ~ element(U_931,powerset(powerset(U_932))) ),
inference(clausify,[status(thm)],[f_250_2]) ).
fof(f_251_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t46_zfmisc_1]) ).
fof(f_251_2,plain,
! [U_934,U_933] :
( set_union2(singleton(U_934),U_933) = U_933
| ~ in(U_934,U_933) ),
inference(variable_rename,[status(thm)],[f_251_1]) ).
cnf(f_251_3,plain,
( set_union2(singleton(U_934),U_933) = U_933
| ~ in(U_934,U_933) ),
inference(clausify,[status(thm)],[f_251_2]) ).
fof(f_252_1,plain,
! [A] :
( ! [B] :
( relation_rng(relation_composition(B,A)) = relation_rng(A)
| ~ subset(relation_dom(A),relation_rng(B))
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t47_relat_1]) ).
fof(f_252_2,plain,
! [U_936] :
( ! [U_935] :
( relation_rng(relation_composition(U_935,U_936)) = relation_rng(U_936)
| ~ subset(relation_dom(U_936),relation_rng(U_935))
| ~ relation(U_935) )
| ~ relation(U_936) ),
inference(variable_rename,[status(thm)],[f_252_1]) ).
cnf(f_252_3,plain,
( relation_rng(relation_composition(U_935,U_936)) = relation_rng(U_936)
| ~ subset(relation_dom(U_936),relation_rng(U_935))
| ~ relation(U_935)
| ~ relation(U_936) ),
inference(clausify,[status(thm)],[f_252_2]) ).
fof(f_253_1,plain,
! [A,B] :
( subset_difference(A,cast_to_subset(A),union_of_subsets(A,B)) = meet_of_subsets(A,complements_of_subsets(A,B))
| B = empty_set
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[t47_setfam_1]) ).
fof(f_253_2,plain,
! [U_938,U_937] :
( subset_difference(U_938,cast_to_subset(U_938),union_of_subsets(U_938,U_937)) = meet_of_subsets(U_938,complements_of_subsets(U_938,U_937))
| U_937 = empty_set
| ~ element(U_937,powerset(powerset(U_938))) ),
inference(variable_rename,[status(thm)],[f_253_1]) ).
cnf(f_253_3,plain,
( subset_difference(U_938,cast_to_subset(U_938),union_of_subsets(U_938,U_937)) = meet_of_subsets(U_938,complements_of_subsets(U_938,U_937))
| U_937 = empty_set
| ~ element(U_937,powerset(powerset(U_938))) ),
inference(clausify,[status(thm)],[f_253_2]) ).
fof(f_254_1,plain,
! [A,B] :
( union_of_subsets(A,complements_of_subsets(A,B)) = subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B))
| B = empty_set
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[t48_setfam_1]) ).
fof(f_254_2,plain,
! [U_940,U_939] :
( union_of_subsets(U_940,complements_of_subsets(U_940,U_939)) = subset_difference(U_940,cast_to_subset(U_940),meet_of_subsets(U_940,U_939))
| U_939 = empty_set
| ~ element(U_939,powerset(powerset(U_940))) ),
inference(variable_rename,[status(thm)],[f_254_1]) ).
cnf(f_254_3,plain,
( union_of_subsets(U_940,complements_of_subsets(U_940,U_939)) = subset_difference(U_940,cast_to_subset(U_940),meet_of_subsets(U_940,U_939))
| U_939 = empty_set
| ~ element(U_939,powerset(powerset(U_940))) ),
inference(clausify,[status(thm)],[f_254_2]) ).
fof(f_255_1,plain,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(fof_nnf,[status(thm)],[t48_xboole_1]) ).
fof(f_255_2,plain,
! [U_942,U_941] : set_difference(U_942,set_difference(U_942,U_941)) = set_intersection2(U_942,U_941),
inference(variable_rename,[status(thm)],[f_255_1]) ).
cnf(f_255_3,plain,
set_difference(U_942,set_difference(U_942,U_941)) = set_intersection2(U_942,U_941),
inference(clausify,[status(thm)],[f_255_2]) ).
fof(f_256_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_256_2,plain,
! [U_943] : set_difference(empty_set,U_943) = empty_set,
inference(variable_rename,[status(thm)],[f_256_1]) ).
cnf(f_256_3,plain,
set_difference(empty_set,U_943) = empty_set,
inference(clausify,[status(thm)],[f_256_2]) ).
fof(f_257_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_257_2,plain,
! [U_946,U_945,U_944] :
( element(U_946,U_944)
| ~ element(U_945,powerset(U_944))
| ~ in(U_946,U_945) ),
inference(variable_rename,[status(thm)],[f_257_1]) ).
cnf(f_257_3,plain,
( element(U_946,U_944)
| ~ element(U_945,powerset(U_944))
| ~ in(U_946,U_945) ),
inference(clausify,[status(thm)],[f_257_2]) ).
fof(f_258_1,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ( ? [C] : in(C,set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t4_xboole_0]) ).
fof(f_258_2,plain,
! [U_950,U_949] :
( ( ~ disjoint(U_950,U_949)
| ! [U_948] : ~ in(U_948,set_intersection2(U_950,U_949)) )
& ( ? [U_947] : in(U_947,set_intersection2(U_950,U_949))
| disjoint(U_950,U_949) ) ),
inference(variable_rename,[status(thm)],[f_258_1]) ).
fof(f_258_3,plain,
( ! [U_954,U_952] :
( ~ disjoint(U_954,U_952)
| ! [U_948] : ~ in(U_948,set_intersection2(U_954,U_952)) )
& ! [U_953,U_951] :
( ? [U_947] : in(U_947,set_intersection2(U_953,U_951))
| disjoint(U_953,U_951) ) ),
inference(miniscope,[status(thm)],[f_258_2]) ).
fof(f_258_4,plain,
( ! [U_954,U_952] :
( ~ disjoint(U_954,U_952)
| ! [U_948] : ~ in(U_948,set_intersection2(U_954,U_952)) )
& ! [U_953,U_951] :
( in(sK141(U_953,U_951),set_intersection2(U_953,U_951))
| disjoint(U_953,U_951) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK141]),skolemize(U_947,sK141(U_953,U_951))],[f_258_3]) ).
cnf(f_258_5,plain,
( in(sK141(U_953,U_951),set_intersection2(U_953,U_951))
| disjoint(U_953,U_951) ),
inference(clausify,[status(thm)],[f_258_4]) ).
cnf(f_258_6,plain,
( ~ disjoint(U_954,U_952)
| ~ in(U_948,set_intersection2(U_954,U_952)) ),
inference(clausify,[status(thm)],[f_258_4]) ).
fof(f_259_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( in(C,subset_complement(A,B))
| in(C,B)
| ~ element(C,A) )
| ~ element(B,powerset(A)) )
| A = empty_set ),
inference(fof_nnf,[status(thm)],[t50_subset_1]) ).
fof(f_259_2,plain,
! [U_957] :
( ! [U_956] :
( ! [U_955] :
( in(U_955,subset_complement(U_957,U_956))
| in(U_955,U_956)
| ~ element(U_955,U_957) )
| ~ element(U_956,powerset(U_957)) )
| U_957 = empty_set ),
inference(variable_rename,[status(thm)],[f_259_1]) ).
cnf(f_259_3,plain,
( in(U_955,subset_complement(U_957,U_956))
| in(U_955,U_956)
| ~ element(U_955,U_957)
| ~ element(U_956,powerset(U_957))
| U_957 = empty_set ),
inference(clausify,[status(thm)],[f_259_2]) ).
fof(f_260_1,plain,
! [A] :
( ! [B] :
( ( ( B = function_inverse(A)
| ? [C,D] :
( ( ( D != apply(B,C)
| ~ in(C,relation_rng(A)) )
& C = apply(A,D)
& in(D,relation_dom(A)) )
| ( ( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& D = apply(B,C)
& in(C,relation_rng(A)) ) )
| relation_dom(B) != relation_rng(A) )
& ( ( ! [C,D] :
( ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
| C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& ( ( C = apply(A,D)
& in(D,relation_dom(A)) )
| D != apply(B,C)
| ~ in(C,relation_rng(A)) ) )
& relation_dom(B) = relation_rng(A) )
| B != function_inverse(A) ) )
| ~ function(B)
| ~ relation(B) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t54_funct_1]) ).
fof(f_260_2,plain,
! [U_963] :
( ! [U_962] :
( ( ( U_962 = function_inverse(U_963)
| ? [U_961,U_960] :
( ( ( U_960 != apply(U_962,U_961)
| ~ in(U_961,relation_rng(U_963)) )
& U_961 = apply(U_963,U_960)
& in(U_960,relation_dom(U_963)) )
| ( ( U_961 != apply(U_963,U_960)
| ~ in(U_960,relation_dom(U_963)) )
& U_960 = apply(U_962,U_961)
& in(U_961,relation_rng(U_963)) ) )
| relation_dom(U_962) != relation_rng(U_963) )
& ( ( ! [U_959,U_958] :
( ( ( U_958 = apply(U_962,U_959)
& in(U_959,relation_rng(U_963)) )
| U_959 != apply(U_963,U_958)
| ~ in(U_958,relation_dom(U_963)) )
& ( ( U_959 = apply(U_963,U_958)
& in(U_958,relation_dom(U_963)) )
| U_958 != apply(U_962,U_959)
| ~ in(U_959,relation_rng(U_963)) ) )
& relation_dom(U_962) = relation_rng(U_963) )
| U_962 != function_inverse(U_963) ) )
| ~ function(U_962)
| ~ relation(U_962) )
| ~ one_to_one(U_963)
| ~ function(U_963)
| ~ relation(U_963) ),
inference(variable_rename,[status(thm)],[f_260_1]) ).
fof(f_260_3,plain,
! [U_963] :
( ! [U_962] :
( ( ( U_962 = function_inverse(U_963)
| ? [U_971,U_969] :
( ( U_969 != apply(U_962,U_971)
| ~ in(U_971,relation_rng(U_963)) )
& U_971 = apply(U_963,U_969)
& in(U_969,relation_dom(U_963)) )
| ? [U_970,U_968] :
( ( U_970 != apply(U_963,U_968)
| ~ in(U_968,relation_dom(U_963)) )
& U_968 = apply(U_962,U_970)
& in(U_970,relation_rng(U_963)) )
| relation_dom(U_962) != relation_rng(U_963) )
& ( ( ! [U_967,U_965] :
( ( U_965 = apply(U_962,U_967)
& in(U_967,relation_rng(U_963)) )
| U_967 != apply(U_963,U_965)
| ~ in(U_965,relation_dom(U_963)) )
& ! [U_966,U_964] :
( ( U_966 = apply(U_963,U_964)
& in(U_964,relation_dom(U_963)) )
| U_964 != apply(U_962,U_966)
| ~ in(U_966,relation_rng(U_963)) )
& relation_dom(U_962) = relation_rng(U_963) )
| U_962 != function_inverse(U_963) ) )
| ~ function(U_962)
| ~ relation(U_962) )
| ~ one_to_one(U_963)
| ~ function(U_963)
| ~ relation(U_963) ),
inference(miniscope,[status(thm)],[f_260_2]) ).
fof(f_260_4,plain,
! [U_963] :
( ! [U_962] :
( ( ( U_962 = function_inverse(U_963)
| ? [U_971,U_969] :
( ( U_969 != apply(U_962,U_971)
| ~ in(U_971,relation_rng(U_963)) )
& U_971 = apply(U_963,U_969)
& in(U_969,relation_dom(U_963)) )
| ? [U_968] :
( ( sK142(U_963,U_962) != apply(U_963,U_968)
| ~ in(U_968,relation_dom(U_963)) )
& U_968 = apply(U_962,sK142(U_963,U_962))
& in(sK142(U_963,U_962),relation_rng(U_963)) )
| relation_dom(U_962) != relation_rng(U_963) )
& ( ( ! [U_967,U_965] :
( ( U_965 = apply(U_962,U_967)
& in(U_967,relation_rng(U_963)) )
| U_967 != apply(U_963,U_965)
| ~ in(U_965,relation_dom(U_963)) )
& ! [U_966,U_964] :
( ( U_966 = apply(U_963,U_964)
& in(U_964,relation_dom(U_963)) )
| U_964 != apply(U_962,U_966)
| ~ in(U_966,relation_rng(U_963)) )
& relation_dom(U_962) = relation_rng(U_963) )
| U_962 != function_inverse(U_963) ) )
| ~ function(U_962)
| ~ relation(U_962) )
| ~ one_to_one(U_963)
| ~ function(U_963)
| ~ relation(U_963) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK142]),skolemize(U_970,sK142(U_963,U_962))],[f_260_3]) ).
fof(f_260_5,plain,
! [U_963] :
( ! [U_962] :
( ( ( U_962 = function_inverse(U_963)
| ? [U_971,U_969] :
( ( U_969 != apply(U_962,U_971)
| ~ in(U_971,relation_rng(U_963)) )
& U_971 = apply(U_963,U_969)
& in(U_969,relation_dom(U_963)) )
| ( ( sK142(U_963,U_962) != apply(U_963,sK143(U_963,U_962))
| ~ in(sK143(U_963,U_962),relation_dom(U_963)) )
& sK143(U_963,U_962) = apply(U_962,sK142(U_963,U_962))
& in(sK142(U_963,U_962),relation_rng(U_963)) )
| relation_dom(U_962) != relation_rng(U_963) )
& ( ( ! [U_967,U_965] :
( ( U_965 = apply(U_962,U_967)
& in(U_967,relation_rng(U_963)) )
| U_967 != apply(U_963,U_965)
| ~ in(U_965,relation_dom(U_963)) )
& ! [U_966,U_964] :
( ( U_966 = apply(U_963,U_964)
& in(U_964,relation_dom(U_963)) )
| U_964 != apply(U_962,U_966)
| ~ in(U_966,relation_rng(U_963)) )
& relation_dom(U_962) = relation_rng(U_963) )
| U_962 != function_inverse(U_963) ) )
| ~ function(U_962)
| ~ relation(U_962) )
| ~ one_to_one(U_963)
| ~ function(U_963)
| ~ relation(U_963) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK143]),skolemize(U_968,sK143(U_963,U_962))],[f_260_4]) ).
fof(f_260_6,plain,
! [U_963] :
( ! [U_962] :
( ( ( U_962 = function_inverse(U_963)
| ? [U_969] :
( ( U_969 != apply(U_962,sK144(U_963,U_962))
| ~ in(sK144(U_963,U_962),relation_rng(U_963)) )
& sK144(U_963,U_962) = apply(U_963,U_969)
& in(U_969,relation_dom(U_963)) )
| ( ( sK142(U_963,U_962) != apply(U_963,sK143(U_963,U_962))
| ~ in(sK143(U_963,U_962),relation_dom(U_963)) )
& sK143(U_963,U_962) = apply(U_962,sK142(U_963,U_962))
& in(sK142(U_963,U_962),relation_rng(U_963)) )
| relation_dom(U_962) != relation_rng(U_963) )
& ( ( ! [U_967,U_965] :
( ( U_965 = apply(U_962,U_967)
& in(U_967,relation_rng(U_963)) )
| U_967 != apply(U_963,U_965)
| ~ in(U_965,relation_dom(U_963)) )
& ! [U_966,U_964] :
( ( U_966 = apply(U_963,U_964)
& in(U_964,relation_dom(U_963)) )
| U_964 != apply(U_962,U_966)
| ~ in(U_966,relation_rng(U_963)) )
& relation_dom(U_962) = relation_rng(U_963) )
| U_962 != function_inverse(U_963) ) )
| ~ function(U_962)
| ~ relation(U_962) )
| ~ one_to_one(U_963)
| ~ function(U_963)
| ~ relation(U_963) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK144]),skolemize(U_971,sK144(U_963,U_962))],[f_260_5]) ).
fof(f_260_7,plain,
! [U_963] :
( ! [U_962] :
( ( ( U_962 = function_inverse(U_963)
| ( ( sK145(U_963,U_962) != apply(U_962,sK144(U_963,U_962))
| ~ in(sK144(U_963,U_962),relation_rng(U_963)) )
& sK144(U_963,U_962) = apply(U_963,sK145(U_963,U_962))
& in(sK145(U_963,U_962),relation_dom(U_963)) )
| ( ( sK142(U_963,U_962) != apply(U_963,sK143(U_963,U_962))
| ~ in(sK143(U_963,U_962),relation_dom(U_963)) )
& sK143(U_963,U_962) = apply(U_962,sK142(U_963,U_962))
& in(sK142(U_963,U_962),relation_rng(U_963)) )
| relation_dom(U_962) != relation_rng(U_963) )
& ( ( ! [U_967,U_965] :
( ( U_965 = apply(U_962,U_967)
& in(U_967,relation_rng(U_963)) )
| U_967 != apply(U_963,U_965)
| ~ in(U_965,relation_dom(U_963)) )
& ! [U_966,U_964] :
( ( U_966 = apply(U_963,U_964)
& in(U_964,relation_dom(U_963)) )
| U_964 != apply(U_962,U_966)
| ~ in(U_966,relation_rng(U_963)) )
& relation_dom(U_962) = relation_rng(U_963) )
| U_962 != function_inverse(U_963) ) )
| ~ function(U_962)
| ~ relation(U_962) )
| ~ one_to_one(U_963)
| ~ function(U_963)
| ~ relation(U_963) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK145]),skolemize(U_969,sK145(U_963,U_962))],[f_260_6]) ).
cnf(f_260_8,plain,
( relation_dom(U_962) = relation_rng(U_963)
| U_962 != function_inverse(U_963)
| ~ function(U_962)
| ~ relation(U_962)
| ~ one_to_one(U_963)
| ~ function(U_963)
| ~ relation(U_963) ),
inference(clausify,[status(thm)],[f_260_7]) ).
cnf(f_260_9,plain,
( in(U_964,relation_dom(U_963))
| U_964 != apply(U_962,U_966)
| ~ in(U_966,relation_rng(U_963))
| U_962 != function_inverse(U_963)
| ~ function(U_962)
| ~ relation(U_962)
| ~ one_to_one(U_963)
| ~ function(U_963)
| ~ relation(U_963) ),
inference(clausify,[status(thm)],[f_260_7]) ).
cnf(f_260_10,plain,
( U_966 = apply(U_963,U_964)
| U_964 != apply(U_962,U_966)
| ~ in(U_966,relation_rng(U_963))
| U_962 != function_inverse(U_963)
| ~ function(U_962)
| ~ relation(U_962)
| ~ one_to_one(U_963)
| ~ function(U_963)
| ~ relation(U_963) ),
inference(clausify,[status(thm)],[f_260_7]) ).
cnf(f_260_11,plain,
( in(U_967,relation_rng(U_963))
| U_967 != apply(U_963,U_965)
| ~ in(U_965,relation_dom(U_963))
| U_962 != function_inverse(U_963)
| ~ function(U_962)
| ~ relation(U_962)
| ~ one_to_one(U_963)
| ~ function(U_963)
| ~ relation(U_963) ),
inference(clausify,[status(thm)],[f_260_7]) ).
cnf(f_260_12,plain,
( U_965 = apply(U_962,U_967)
| U_967 != apply(U_963,U_965)
| ~ in(U_965,relation_dom(U_963))
| U_962 != function_inverse(U_963)
| ~ function(U_962)
| ~ relation(U_962)
| ~ one_to_one(U_963)
| ~ function(U_963)
| ~ relation(U_963) ),
inference(clausify,[status(thm)],[f_260_7]) ).
cnf(f_260_13,plain,
( in(sK145(U_963,U_962),relation_dom(U_963))
| in(sK142(U_963,U_962),relation_rng(U_963))
| relation_dom(U_962) != relation_rng(U_963)
| U_962 = function_inverse(U_963)
| ~ function(U_962)
| ~ relation(U_962)
| ~ one_to_one(U_963)
| ~ function(U_963)
| ~ relation(U_963) ),
inference(clausify,[status(thm)],[f_260_7]) ).
cnf(f_260_14,plain,
( sK144(U_963,U_962) = apply(U_963,sK145(U_963,U_962))
| in(sK142(U_963,U_962),relation_rng(U_963))
| relation_dom(U_962) != relation_rng(U_963)
| U_962 = function_inverse(U_963)
| ~ function(U_962)
| ~ relation(U_962)
| ~ one_to_one(U_963)
| ~ function(U_963)
| ~ relation(U_963) ),
inference(clausify,[status(thm)],[f_260_7]) ).
cnf(f_260_15,plain,
( in(sK145(U_963,U_962),relation_dom(U_963))
| sK143(U_963,U_962) = apply(U_962,sK142(U_963,U_962))
| relation_dom(U_962) != relation_rng(U_963)
| U_962 = function_inverse(U_963)
| ~ function(U_962)
| ~ relation(U_962)
| ~ one_to_one(U_963)
| ~ function(U_963)
| ~ relation(U_963) ),
inference(clausify,[status(thm)],[f_260_7]) ).
cnf(f_260_16,plain,
( sK144(U_963,U_962) = apply(U_963,sK145(U_963,U_962))
| sK143(U_963,U_962) = apply(U_962,sK142(U_963,U_962))
| relation_dom(U_962) != relation_rng(U_963)
| U_962 = function_inverse(U_963)
| ~ function(U_962)
| ~ relation(U_962)
| ~ one_to_one(U_963)
| ~ function(U_963)
| ~ relation(U_963) ),
inference(clausify,[status(thm)],[f_260_7]) ).
cnf(f_260_17,plain,
( in(sK142(U_963,U_962),relation_rng(U_963))
| sK145(U_963,U_962) != apply(U_962,sK144(U_963,U_962))
| ~ in(sK144(U_963,U_962),relation_rng(U_963))
| relation_dom(U_962) != relation_rng(U_963)
| U_962 = function_inverse(U_963)
| ~ function(U_962)
| ~ relation(U_962)
| ~ one_to_one(U_963)
| ~ function(U_963)
| ~ relation(U_963) ),
inference(clausify,[status(thm)],[f_260_7]) ).
cnf(f_260_18,plain,
( sK143(U_963,U_962) = apply(U_962,sK142(U_963,U_962))
| sK145(U_963,U_962) != apply(U_962,sK144(U_963,U_962))
| ~ in(sK144(U_963,U_962),relation_rng(U_963))
| relation_dom(U_962) != relation_rng(U_963)
| U_962 = function_inverse(U_963)
| ~ function(U_962)
| ~ relation(U_962)
| ~ one_to_one(U_963)
| ~ function(U_963)
| ~ relation(U_963) ),
inference(clausify,[status(thm)],[f_260_7]) ).
cnf(f_260_19,plain,
( in(sK145(U_963,U_962),relation_dom(U_963))
| sK142(U_963,U_962) != apply(U_963,sK143(U_963,U_962))
| ~ in(sK143(U_963,U_962),relation_dom(U_963))
| relation_dom(U_962) != relation_rng(U_963)
| U_962 = function_inverse(U_963)
| ~ function(U_962)
| ~ relation(U_962)
| ~ one_to_one(U_963)
| ~ function(U_963)
| ~ relation(U_963) ),
inference(clausify,[status(thm)],[f_260_7]) ).
cnf(f_260_20,plain,
( sK144(U_963,U_962) = apply(U_963,sK145(U_963,U_962))
| sK142(U_963,U_962) != apply(U_963,sK143(U_963,U_962))
| ~ in(sK143(U_963,U_962),relation_dom(U_963))
| relation_dom(U_962) != relation_rng(U_963)
| U_962 = function_inverse(U_963)
| ~ function(U_962)
| ~ relation(U_962)
| ~ one_to_one(U_963)
| ~ function(U_963)
| ~ relation(U_963) ),
inference(clausify,[status(thm)],[f_260_7]) ).
cnf(f_260_21,plain,
( sK145(U_963,U_962) != apply(U_962,sK144(U_963,U_962))
| ~ in(sK144(U_963,U_962),relation_rng(U_963))
| sK142(U_963,U_962) != apply(U_963,sK143(U_963,U_962))
| ~ in(sK143(U_963,U_962),relation_dom(U_963))
| relation_dom(U_962) != relation_rng(U_963)
| U_962 = function_inverse(U_963)
| ~ function(U_962)
| ~ relation(U_962)
| ~ one_to_one(U_963)
| ~ function(U_963)
| ~ relation(U_963) ),
inference(clausify,[status(thm)],[f_260_7]) ).
fof(f_261_1,plain,
! [A,B,C] :
( ~ in(B,C)
| ~ in(B,subset_complement(A,C))
| ~ element(C,powerset(A)) ),
inference(fof_nnf,[status(thm)],[t54_subset_1]) ).
fof(f_261_2,plain,
! [U_974,U_973,U_972] :
( ~ in(U_973,U_972)
| ~ in(U_973,subset_complement(U_974,U_972))
| ~ element(U_972,powerset(U_974)) ),
inference(variable_rename,[status(thm)],[f_261_1]) ).
cnf(f_261_3,plain,
( ~ in(U_973,U_972)
| ~ in(U_973,subset_complement(U_974,U_972))
| ~ element(U_972,powerset(U_974)) ),
inference(clausify,[status(thm)],[f_261_2]) ).
fof(f_262_1,plain,
! [A] :
( ( relation_dom(A) = relation_rng(function_inverse(A))
& relation_rng(A) = relation_dom(function_inverse(A)) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t55_funct_1]) ).
fof(f_262_2,plain,
! [U_975] :
( ( relation_dom(U_975) = relation_rng(function_inverse(U_975))
& relation_rng(U_975) = relation_dom(function_inverse(U_975)) )
| ~ one_to_one(U_975)
| ~ function(U_975)
| ~ relation(U_975) ),
inference(variable_rename,[status(thm)],[f_262_1]) ).
cnf(f_262_3,plain,
( relation_rng(U_975) = relation_dom(function_inverse(U_975))
| ~ one_to_one(U_975)
| ~ function(U_975)
| ~ relation(U_975) ),
inference(clausify,[status(thm)],[f_262_2]) ).
cnf(f_262_4,plain,
( relation_dom(U_975) = relation_rng(function_inverse(U_975))
| ~ one_to_one(U_975)
| ~ function(U_975)
| ~ relation(U_975) ),
inference(clausify,[status(thm)],[f_262_2]) ).
fof(f_263_1,plain,
! [A] :
( A = empty_set
| ? [B,C] : in(ordered_pair(B,C),A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t56_relat_1]) ).
fof(f_263_2,plain,
! [U_978] :
( U_978 = empty_set
| ? [U_977,U_976] : in(ordered_pair(U_977,U_976),U_978)
| ~ relation(U_978) ),
inference(variable_rename,[status(thm)],[f_263_1]) ).
fof(f_263_3,plain,
! [U_978] :
( U_978 = empty_set
| ? [U_976] : in(ordered_pair(sK146(U_978),U_976),U_978)
| ~ relation(U_978) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK146]),skolemize(U_977,sK146(U_978))],[f_263_2]) ).
fof(f_263_4,plain,
! [U_978] :
( U_978 = empty_set
| in(ordered_pair(sK146(U_978),sK147(U_978)),U_978)
| ~ relation(U_978) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK147]),skolemize(U_976,sK147(U_978))],[f_263_3]) ).
cnf(f_263_5,plain,
( U_978 = empty_set
| in(ordered_pair(sK146(U_978),sK147(U_978)),U_978)
| ~ relation(U_978) ),
inference(clausify,[status(thm)],[f_263_4]) ).
fof(f_264_1,plain,
! [A,B] :
( ( A = apply(relation_composition(function_inverse(B),B),A)
& A = apply(B,apply(function_inverse(B),A)) )
| ~ in(A,relation_rng(B))
| ~ one_to_one(B)
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t57_funct_1]) ).
fof(f_264_2,plain,
! [U_980,U_979] :
( ( U_980 = apply(relation_composition(function_inverse(U_979),U_979),U_980)
& U_980 = apply(U_979,apply(function_inverse(U_979),U_980)) )
| ~ in(U_980,relation_rng(U_979))
| ~ one_to_one(U_979)
| ~ function(U_979)
| ~ relation(U_979) ),
inference(variable_rename,[status(thm)],[f_264_1]) ).
cnf(f_264_3,plain,
( U_980 = apply(U_979,apply(function_inverse(U_979),U_980))
| ~ in(U_980,relation_rng(U_979))
| ~ one_to_one(U_979)
| ~ function(U_979)
| ~ relation(U_979) ),
inference(clausify,[status(thm)],[f_264_2]) ).
cnf(f_264_4,plain,
( U_980 = apply(relation_composition(function_inverse(U_979),U_979),U_980)
| ~ in(U_980,relation_rng(U_979))
| ~ one_to_one(U_979)
| ~ function(U_979)
| ~ relation(U_979) ),
inference(clausify,[status(thm)],[f_264_2]) ).
fof(f_265_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_265_2,plain,
! [U_983,U_982,U_981] :
( ~ empty(U_981)
| ~ element(U_982,powerset(U_981))
| ~ in(U_983,U_982) ),
inference(variable_rename,[status(thm)],[f_265_1]) ).
fof(f_265_3,plain,
! [U_983,U_982] :
( ! [U_981] :
( ~ empty(U_981)
| ~ element(U_982,powerset(U_981)) )
| ~ in(U_983,U_982) ),
inference(miniscope,[status(thm)],[f_265_2]) ).
cnf(f_265_4,plain,
( ~ empty(U_981)
| ~ element(U_982,powerset(U_981))
| ~ in(U_983,U_982) ),
inference(clausify,[status(thm)],[f_265_3]) ).
fof(f_266_1,plain,
! [A] :
( ( ( well_founded_relation(A)
| ~ is_well_founded_in(A,relation_field(A)) )
& ( is_well_founded_in(A,relation_field(A))
| ~ well_founded_relation(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t5_wellord1]) ).
fof(f_266_2,plain,
! [U_984] :
( ( ( well_founded_relation(U_984)
| ~ is_well_founded_in(U_984,relation_field(U_984)) )
& ( is_well_founded_in(U_984,relation_field(U_984))
| ~ well_founded_relation(U_984) ) )
| ~ relation(U_984) ),
inference(variable_rename,[status(thm)],[f_266_1]) ).
cnf(f_266_3,plain,
( is_well_founded_in(U_984,relation_field(U_984))
| ~ well_founded_relation(U_984)
| ~ relation(U_984) ),
inference(clausify,[status(thm)],[f_266_2]) ).
cnf(f_266_4,plain,
( well_founded_relation(U_984)
| ~ is_well_founded_in(U_984,relation_field(U_984))
| ~ relation(U_984) ),
inference(clausify,[status(thm)],[f_266_2]) ).
fof(f_267_1,plain,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(fof_nnf,[status(thm)],[t60_relat_1]) ).
cnf(f_267_2,plain,
relation_dom(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_267_1]) ).
cnf(f_267_3,plain,
relation_rng(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_267_1]) ).
fof(f_268_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t60_xboole_1]) ).
fof(f_268_2,plain,
! [U_986,U_985] :
( ~ proper_subset(U_985,U_986)
| ~ subset(U_986,U_985) ),
inference(variable_rename,[status(thm)],[f_268_1]) ).
cnf(f_268_3,plain,
( ~ proper_subset(U_985,U_986)
| ~ subset(U_986,U_985) ),
inference(clausify,[status(thm)],[f_268_2]) ).
fof(f_269_1,plain,
! [A] :
( one_to_one(function_inverse(A))
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t62_funct_1]) ).
fof(f_269_2,plain,
! [U_987] :
( one_to_one(function_inverse(U_987))
| ~ one_to_one(U_987)
| ~ function(U_987)
| ~ relation(U_987) ),
inference(variable_rename,[status(thm)],[f_269_1]) ).
cnf(f_269_3,plain,
( one_to_one(function_inverse(U_987))
| ~ one_to_one(U_987)
| ~ function(U_987)
| ~ relation(U_987) ),
inference(clausify,[status(thm)],[f_269_2]) ).
fof(f_270_1,plain,
! [A,B,C] :
( disjoint(A,C)
| ~ disjoint(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t63_xboole_1]) ).
fof(f_270_2,plain,
! [U_990,U_989,U_988] :
( disjoint(U_990,U_988)
| ~ disjoint(U_989,U_988)
| ~ subset(U_990,U_989) ),
inference(variable_rename,[status(thm)],[f_270_1]) ).
cnf(f_270_3,plain,
( disjoint(U_990,U_988)
| ~ disjoint(U_989,U_988)
| ~ subset(U_990,U_989) ),
inference(clausify,[status(thm)],[f_270_2]) ).
fof(f_271_1,plain,
! [A] :
( A = empty_set
| ( relation_rng(A) != empty_set
& relation_dom(A) != empty_set )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t64_relat_1]) ).
fof(f_271_2,plain,
! [U_991] :
( U_991 = empty_set
| ( relation_rng(U_991) != empty_set
& relation_dom(U_991) != empty_set )
| ~ relation(U_991) ),
inference(variable_rename,[status(thm)],[f_271_1]) ).
cnf(f_271_3,plain,
( relation_dom(U_991) != empty_set
| U_991 = empty_set
| ~ relation(U_991) ),
inference(clausify,[status(thm)],[f_271_2]) ).
cnf(f_271_4,plain,
( relation_rng(U_991) != empty_set
| U_991 = empty_set
| ~ relation(U_991) ),
inference(clausify,[status(thm)],[f_271_2]) ).
fof(f_272_1,plain,
! [A] :
( ( ( relation_dom(A) = empty_set
| relation_rng(A) != empty_set )
& ( relation_rng(A) = empty_set
| relation_dom(A) != empty_set ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t65_relat_1]) ).
fof(f_272_2,plain,
! [U_992] :
( ( ( relation_dom(U_992) = empty_set
| relation_rng(U_992) != empty_set )
& ( relation_rng(U_992) = empty_set
| relation_dom(U_992) != empty_set ) )
| ~ relation(U_992) ),
inference(variable_rename,[status(thm)],[f_272_1]) ).
cnf(f_272_3,plain,
( relation_rng(U_992) = empty_set
| relation_dom(U_992) != empty_set
| ~ relation(U_992) ),
inference(clausify,[status(thm)],[f_272_2]) ).
cnf(f_272_4,plain,
( relation_dom(U_992) = empty_set
| relation_rng(U_992) != empty_set
| ~ relation(U_992) ),
inference(clausify,[status(thm)],[f_272_2]) ).
fof(f_273_1,plain,
! [A,B] :
( ( set_difference(A,singleton(B)) = A
| in(B,A) )
& ( ~ in(B,A)
| set_difference(A,singleton(B)) != A ) ),
inference(fof_nnf,[status(thm)],[t65_zfmisc_1]) ).
fof(f_273_2,plain,
! [U_994,U_993] :
( ( set_difference(U_994,singleton(U_993)) = U_994
| in(U_993,U_994) )
& ( ~ in(U_993,U_994)
| set_difference(U_994,singleton(U_993)) != U_994 ) ),
inference(variable_rename,[status(thm)],[f_273_1]) ).
fof(f_273_3,plain,
( ! [U_998,U_996] :
( set_difference(U_998,singleton(U_996)) = U_998
| in(U_996,U_998) )
& ! [U_997,U_995] :
( ~ in(U_995,U_997)
| set_difference(U_997,singleton(U_995)) != U_997 ) ),
inference(miniscope,[status(thm)],[f_273_2]) ).
cnf(f_273_4,plain,
( ~ in(U_995,U_997)
| set_difference(U_997,singleton(U_995)) != U_997 ),
inference(clausify,[status(thm)],[f_273_3]) ).
cnf(f_273_5,plain,
( set_difference(U_998,singleton(U_996)) = U_998
| in(U_996,U_998) ),
inference(clausify,[status(thm)],[f_273_3]) ).
fof(f_274_1,plain,
! [A,B] :
( ! [C] :
( ( ( B = relation_dom_restriction(C,A)
| ? [D] :
( apply(B,D) != apply(C,D)
& in(D,relation_dom(B)) )
| relation_dom(B) != set_intersection2(relation_dom(C),A) )
& ( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) )
| B != relation_dom_restriction(C,A) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t68_funct_1]) ).
fof(f_274_2,plain,
! [U_1003,U_1002] :
( ! [U_1001] :
( ( ( U_1002 = relation_dom_restriction(U_1001,U_1003)
| ? [U_1000] :
( apply(U_1002,U_1000) != apply(U_1001,U_1000)
& in(U_1000,relation_dom(U_1002)) )
| relation_dom(U_1002) != set_intersection2(relation_dom(U_1001),U_1003) )
& ( ( ! [U_999] :
( apply(U_1002,U_999) = apply(U_1001,U_999)
| ~ in(U_999,relation_dom(U_1002)) )
& relation_dom(U_1002) = set_intersection2(relation_dom(U_1001),U_1003) )
| U_1002 != relation_dom_restriction(U_1001,U_1003) ) )
| ~ function(U_1001)
| ~ relation(U_1001) )
| ~ function(U_1002)
| ~ relation(U_1002) ),
inference(variable_rename,[status(thm)],[f_274_1]) ).
fof(f_274_3,plain,
! [U_1003,U_1002] :
( ! [U_1001] :
( ( ( U_1002 = relation_dom_restriction(U_1001,U_1003)
| ( apply(U_1002,sK148(U_1003,U_1002,U_1001)) != apply(U_1001,sK148(U_1003,U_1002,U_1001))
& in(sK148(U_1003,U_1002,U_1001),relation_dom(U_1002)) )
| relation_dom(U_1002) != set_intersection2(relation_dom(U_1001),U_1003) )
& ( ( ! [U_999] :
( apply(U_1002,U_999) = apply(U_1001,U_999)
| ~ in(U_999,relation_dom(U_1002)) )
& relation_dom(U_1002) = set_intersection2(relation_dom(U_1001),U_1003) )
| U_1002 != relation_dom_restriction(U_1001,U_1003) ) )
| ~ function(U_1001)
| ~ relation(U_1001) )
| ~ function(U_1002)
| ~ relation(U_1002) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK148]),skolemize(U_1000,sK148(U_1003,U_1002,U_1001))],[f_274_2]) ).
cnf(f_274_4,plain,
( relation_dom(U_1002) = set_intersection2(relation_dom(U_1001),U_1003)
| U_1002 != relation_dom_restriction(U_1001,U_1003)
| ~ function(U_1001)
| ~ relation(U_1001)
| ~ function(U_1002)
| ~ relation(U_1002) ),
inference(clausify,[status(thm)],[f_274_3]) ).
cnf(f_274_5,plain,
( apply(U_1002,U_999) = apply(U_1001,U_999)
| ~ in(U_999,relation_dom(U_1002))
| U_1002 != relation_dom_restriction(U_1001,U_1003)
| ~ function(U_1001)
| ~ relation(U_1001)
| ~ function(U_1002)
| ~ relation(U_1002) ),
inference(clausify,[status(thm)],[f_274_3]) ).
cnf(f_274_6,plain,
( in(sK148(U_1003,U_1002,U_1001),relation_dom(U_1002))
| relation_dom(U_1002) != set_intersection2(relation_dom(U_1001),U_1003)
| U_1002 = relation_dom_restriction(U_1001,U_1003)
| ~ function(U_1001)
| ~ relation(U_1001)
| ~ function(U_1002)
| ~ relation(U_1002) ),
inference(clausify,[status(thm)],[f_274_3]) ).
cnf(f_274_7,plain,
( apply(U_1002,sK148(U_1003,U_1002,U_1001)) != apply(U_1001,sK148(U_1003,U_1002,U_1001))
| relation_dom(U_1002) != set_intersection2(relation_dom(U_1001),U_1003)
| U_1002 = relation_dom_restriction(U_1001,U_1003)
| ~ function(U_1001)
| ~ relation(U_1001)
| ~ function(U_1002)
| ~ relation(U_1002) ),
inference(clausify,[status(thm)],[f_274_3]) ).
fof(f_275_1,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(fof_nnf,[status(thm)],[t69_enumset1]) ).
fof(f_275_2,plain,
! [U_1004] : unordered_pair(U_1004,U_1004) = singleton(U_1004),
inference(variable_rename,[status(thm)],[f_275_1]) ).
cnf(f_275_3,plain,
unordered_pair(U_1004,U_1004) = singleton(U_1004),
inference(clausify,[status(thm)],[f_275_2]) ).
fof(f_276_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_276_2,plain,
! [U_1005] :
( U_1005 = empty_set
| ~ empty(U_1005) ),
inference(variable_rename,[status(thm)],[f_276_1]) ).
cnf(f_276_3,plain,
( U_1005 = empty_set
| ~ empty(U_1005) ),
inference(clausify,[status(thm)],[f_276_2]) ).
fof(f_277_1,plain,
! [A,B] :
( A = B
| ~ subset(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t6_zfmisc_1]) ).
fof(f_277_2,plain,
! [U_1007,U_1006] :
( U_1007 = U_1006
| ~ subset(singleton(U_1007),singleton(U_1006)) ),
inference(variable_rename,[status(thm)],[f_277_1]) ).
cnf(f_277_3,plain,
( U_1007 = U_1006
| ~ subset(singleton(U_1007),singleton(U_1006)) ),
inference(clausify,[status(thm)],[f_277_2]) ).
fof(f_278_1,plain,
! [A,B,C] :
( apply(relation_dom_restriction(C,A),B) = apply(C,B)
| ~ in(B,relation_dom(relation_dom_restriction(C,A)))
| ~ function(C)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t70_funct_1]) ).
fof(f_278_2,plain,
! [U_1010,U_1009,U_1008] :
( apply(relation_dom_restriction(U_1008,U_1010),U_1009) = apply(U_1008,U_1009)
| ~ in(U_1009,relation_dom(relation_dom_restriction(U_1008,U_1010)))
| ~ function(U_1008)
| ~ relation(U_1008) ),
inference(variable_rename,[status(thm)],[f_278_1]) ).
cnf(f_278_3,plain,
( apply(relation_dom_restriction(U_1008,U_1010),U_1009) = apply(U_1008,U_1009)
| ~ in(U_1009,relation_dom(relation_dom_restriction(U_1008,U_1010)))
| ~ function(U_1008)
| ~ relation(U_1008) ),
inference(clausify,[status(thm)],[f_278_2]) ).
fof(f_279_1,plain,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
inference(fof_nnf,[status(thm)],[t71_relat_1]) ).
fof(f_279_2,plain,
! [U_1011] :
( relation_rng(identity_relation(U_1011)) = U_1011
& relation_dom(identity_relation(U_1011)) = U_1011 ),
inference(variable_rename,[status(thm)],[f_279_1]) ).
fof(f_279_3,plain,
( ! [U_1013] : relation_rng(identity_relation(U_1013)) = U_1013
& ! [U_1012] : relation_dom(identity_relation(U_1012)) = U_1012 ),
inference(miniscope,[status(thm)],[f_279_2]) ).
cnf(f_279_4,plain,
relation_dom(identity_relation(U_1012)) = U_1012,
inference(clausify,[status(thm)],[f_279_3]) ).
cnf(f_279_5,plain,
relation_rng(identity_relation(U_1013)) = U_1013,
inference(clausify,[status(thm)],[f_279_3]) ).
fof(f_280_1,plain,
! [A,B,C] :
( apply(relation_dom_restriction(C,A),B) = apply(C,B)
| ~ in(B,A)
| ~ function(C)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t72_funct_1]) ).
fof(f_280_2,plain,
! [U_1016,U_1015,U_1014] :
( apply(relation_dom_restriction(U_1014,U_1016),U_1015) = apply(U_1014,U_1015)
| ~ in(U_1015,U_1016)
| ~ function(U_1014)
| ~ relation(U_1014) ),
inference(variable_rename,[status(thm)],[f_280_1]) ).
cnf(f_280_3,plain,
( apply(relation_dom_restriction(U_1014,U_1016),U_1015) = apply(U_1014,U_1015)
| ~ in(U_1015,U_1016)
| ~ function(U_1014)
| ~ relation(U_1014) ),
inference(clausify,[status(thm)],[f_280_2]) ).
fof(f_281_1,plain,
! [A,B,C,D] :
( ( ( in(ordered_pair(A,B),relation_composition(identity_relation(C),D))
| ~ in(ordered_pair(A,B),D)
| ~ in(A,C) )
& ( ( in(ordered_pair(A,B),D)
& in(A,C) )
| ~ in(ordered_pair(A,B),relation_composition(identity_relation(C),D)) ) )
| ~ relation(D) ),
inference(fof_nnf,[status(thm)],[t74_relat_1]) ).
fof(f_281_2,plain,
! [U_1020,U_1019,U_1018,U_1017] :
( ( ( in(ordered_pair(U_1020,U_1019),relation_composition(identity_relation(U_1018),U_1017))
| ~ in(ordered_pair(U_1020,U_1019),U_1017)
| ~ in(U_1020,U_1018) )
& ( ( in(ordered_pair(U_1020,U_1019),U_1017)
& in(U_1020,U_1018) )
| ~ in(ordered_pair(U_1020,U_1019),relation_composition(identity_relation(U_1018),U_1017)) ) )
| ~ relation(U_1017) ),
inference(variable_rename,[status(thm)],[f_281_1]) ).
cnf(f_281_3,plain,
( in(U_1020,U_1018)
| ~ in(ordered_pair(U_1020,U_1019),relation_composition(identity_relation(U_1018),U_1017))
| ~ relation(U_1017) ),
inference(clausify,[status(thm)],[f_281_2]) ).
cnf(f_281_4,plain,
( in(ordered_pair(U_1020,U_1019),U_1017)
| ~ in(ordered_pair(U_1020,U_1019),relation_composition(identity_relation(U_1018),U_1017))
| ~ relation(U_1017) ),
inference(clausify,[status(thm)],[f_281_2]) ).
cnf(f_281_5,plain,
( in(ordered_pair(U_1020,U_1019),relation_composition(identity_relation(U_1018),U_1017))
| ~ in(ordered_pair(U_1020,U_1019),U_1017)
| ~ in(U_1020,U_1018)
| ~ relation(U_1017) ),
inference(clausify,[status(thm)],[f_281_2]) ).
fof(f_282_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_282_2,plain,
! [U_1022,U_1021] :
( ~ empty(U_1021)
| ~ in(U_1022,U_1021) ),
inference(variable_rename,[status(thm)],[f_282_1]) ).
cnf(f_282_3,plain,
( ~ empty(U_1021)
| ~ in(U_1022,U_1021) ),
inference(clausify,[status(thm)],[f_282_2]) ).
fof(f_283_1,plain,
! [A,B] :
( ? [C] :
( ! [D] :
( ~ in(D,C)
| ~ in(D,B) )
& in(C,B) )
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_tarski]) ).
fof(f_283_2,plain,
! [U_1026,U_1025] :
( ? [U_1024] :
( ! [U_1023] :
( ~ in(U_1023,U_1024)
| ~ in(U_1023,U_1025) )
& in(U_1024,U_1025) )
| ~ in(U_1026,U_1025) ),
inference(variable_rename,[status(thm)],[f_283_1]) ).
fof(f_283_3,plain,
! [U_1026,U_1025] :
( ( ! [U_1023] :
( ~ in(U_1023,sK149(U_1026,U_1025))
| ~ in(U_1023,U_1025) )
& in(sK149(U_1026,U_1025),U_1025) )
| ~ in(U_1026,U_1025) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK149]),skolemize(U_1024,sK149(U_1026,U_1025))],[f_283_2]) ).
cnf(f_283_4,plain,
( in(sK149(U_1026,U_1025),U_1025)
| ~ in(U_1026,U_1025) ),
inference(clausify,[status(thm)],[f_283_3]) ).
cnf(f_283_5,plain,
( ~ in(U_1023,sK149(U_1026,U_1025))
| ~ in(U_1023,U_1025)
| ~ in(U_1026,U_1025) ),
inference(clausify,[status(thm)],[f_283_3]) ).
fof(f_284_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1]) ).
fof(f_284_2,plain,
! [U_1028,U_1027] : subset(U_1028,set_union2(U_1028,U_1027)),
inference(variable_rename,[status(thm)],[f_284_1]) ).
cnf(f_284_3,plain,
subset(U_1028,set_union2(U_1028,U_1027)),
inference(clausify,[status(thm)],[f_284_2]) ).
fof(f_285_1,plain,
! [A,B] :
( ( disjoint(A,B)
| set_difference(A,B) != A )
& ( set_difference(A,B) = A
| ~ disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t83_xboole_1]) ).
fof(f_285_2,plain,
! [U_1030,U_1029] :
( ( disjoint(U_1030,U_1029)
| set_difference(U_1030,U_1029) != U_1030 )
& ( set_difference(U_1030,U_1029) = U_1030
| ~ disjoint(U_1030,U_1029) ) ),
inference(variable_rename,[status(thm)],[f_285_1]) ).
fof(f_285_3,plain,
( ! [U_1034,U_1032] :
( disjoint(U_1034,U_1032)
| set_difference(U_1034,U_1032) != U_1034 )
& ! [U_1033,U_1031] :
( set_difference(U_1033,U_1031) = U_1033
| ~ disjoint(U_1033,U_1031) ) ),
inference(miniscope,[status(thm)],[f_285_2]) ).
cnf(f_285_4,plain,
( set_difference(U_1033,U_1031) = U_1033
| ~ disjoint(U_1033,U_1031) ),
inference(clausify,[status(thm)],[f_285_3]) ).
cnf(f_285_5,plain,
( disjoint(U_1034,U_1032)
| set_difference(U_1034,U_1032) != U_1034 ),
inference(clausify,[status(thm)],[f_285_3]) ).
fof(f_286_1,plain,
! [A,B,C] :
( ( ( in(A,relation_dom(relation_dom_restriction(C,B)))
| ~ in(A,relation_dom(C))
| ~ in(A,B) )
& ( ( in(A,relation_dom(C))
& in(A,B) )
| ~ in(A,relation_dom(relation_dom_restriction(C,B))) ) )
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t86_relat_1]) ).
fof(f_286_2,plain,
! [U_1037,U_1036,U_1035] :
( ( ( in(U_1037,relation_dom(relation_dom_restriction(U_1035,U_1036)))
| ~ in(U_1037,relation_dom(U_1035))
| ~ in(U_1037,U_1036) )
& ( ( in(U_1037,relation_dom(U_1035))
& in(U_1037,U_1036) )
| ~ in(U_1037,relation_dom(relation_dom_restriction(U_1035,U_1036))) ) )
| ~ relation(U_1035) ),
inference(variable_rename,[status(thm)],[f_286_1]) ).
cnf(f_286_3,plain,
( in(U_1037,U_1036)
| ~ in(U_1037,relation_dom(relation_dom_restriction(U_1035,U_1036)))
| ~ relation(U_1035) ),
inference(clausify,[status(thm)],[f_286_2]) ).
cnf(f_286_4,plain,
( in(U_1037,relation_dom(U_1035))
| ~ in(U_1037,relation_dom(relation_dom_restriction(U_1035,U_1036)))
| ~ relation(U_1035) ),
inference(clausify,[status(thm)],[f_286_2]) ).
cnf(f_286_5,plain,
( in(U_1037,relation_dom(relation_dom_restriction(U_1035,U_1036)))
| ~ in(U_1037,relation_dom(U_1035))
| ~ in(U_1037,U_1036)
| ~ relation(U_1035) ),
inference(clausify,[status(thm)],[f_286_2]) ).
fof(f_287_1,plain,
! [A,B] :
( subset(relation_dom_restriction(B,A),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t88_relat_1]) ).
fof(f_287_2,plain,
! [U_1039,U_1038] :
( subset(relation_dom_restriction(U_1038,U_1039),U_1038)
| ~ relation(U_1038) ),
inference(variable_rename,[status(thm)],[f_287_1]) ).
cnf(f_287_3,plain,
( subset(relation_dom_restriction(U_1038,U_1039),U_1038)
| ~ relation(U_1038) ),
inference(clausify,[status(thm)],[f_287_2]) ).
fof(f_288_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_288_2,plain,
! [U_1041,U_1040] :
( ~ empty(U_1040)
| U_1041 = U_1040
| ~ empty(U_1041) ),
inference(variable_rename,[status(thm)],[f_288_1]) ).
fof(f_288_3,plain,
! [U_1041] :
( ! [U_1040] :
( ~ empty(U_1040)
| U_1041 = U_1040 )
| ~ empty(U_1041) ),
inference(miniscope,[status(thm)],[f_288_2]) ).
cnf(f_288_4,plain,
( ~ empty(U_1040)
| U_1041 = U_1040
| ~ empty(U_1041) ),
inference(clausify,[status(thm)],[f_288_3]) ).
fof(f_289_1,plain,
! [A,B,C] :
( ( ( in(ordered_pair(A,B),C)
| B != apply(C,A)
| ~ in(A,relation_dom(C)) )
& ( ( B = apply(C,A)
& in(A,relation_dom(C)) )
| ~ in(ordered_pair(A,B),C) ) )
| ~ function(C)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t8_funct_1]) ).
fof(f_289_2,plain,
! [U_1044,U_1043,U_1042] :
( ( ( in(ordered_pair(U_1044,U_1043),U_1042)
| U_1043 != apply(U_1042,U_1044)
| ~ in(U_1044,relation_dom(U_1042)) )
& ( ( U_1043 = apply(U_1042,U_1044)
& in(U_1044,relation_dom(U_1042)) )
| ~ in(ordered_pair(U_1044,U_1043),U_1042) ) )
| ~ function(U_1042)
| ~ relation(U_1042) ),
inference(variable_rename,[status(thm)],[f_289_1]) ).
cnf(f_289_3,plain,
( in(U_1044,relation_dom(U_1042))
| ~ in(ordered_pair(U_1044,U_1043),U_1042)
| ~ function(U_1042)
| ~ relation(U_1042) ),
inference(clausify,[status(thm)],[f_289_2]) ).
cnf(f_289_4,plain,
( U_1043 = apply(U_1042,U_1044)
| ~ in(ordered_pair(U_1044,U_1043),U_1042)
| ~ function(U_1042)
| ~ relation(U_1042) ),
inference(clausify,[status(thm)],[f_289_2]) ).
cnf(f_289_5,plain,
( in(ordered_pair(U_1044,U_1043),U_1042)
| U_1043 != apply(U_1042,U_1044)
| ~ in(U_1044,relation_dom(U_1042))
| ~ function(U_1042)
| ~ relation(U_1042) ),
inference(clausify,[status(thm)],[f_289_2]) ).
fof(f_290_1,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( well_orders(A,relation_field(A))
<=> well_ordering(A) ) ),
inference(negate,[status(cth)],[t8_wellord1]) ).
fof(f_290_2,negated_conjecture,
? [A] :
( ( ( ~ well_orders(A,relation_field(A))
& well_ordering(A) )
| ( ~ well_ordering(A)
& well_orders(A,relation_field(A)) ) )
& relation(A) ),
inference(fof_nnf,[status(thm)],[f_290_1]) ).
fof(f_290_3,negated_conjecture,
? [U_1045] :
( ( ( ~ well_orders(U_1045,relation_field(U_1045))
& well_ordering(U_1045) )
| ( ~ well_ordering(U_1045)
& well_orders(U_1045,relation_field(U_1045)) ) )
& relation(U_1045) ),
inference(variable_rename,[status(thm)],[f_290_2]) ).
fof(f_290_4,negated_conjecture,
( ( ( ~ well_orders(sK150,relation_field(sK150))
& well_ordering(sK150) )
| ( ~ well_ordering(sK150)
& well_orders(sK150,relation_field(sK150)) ) )
& relation(sK150) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK150]),skolemize(U_1045,sK150)],[f_290_3]) ).
cnf(f_290_5,negated_conjecture,
relation(sK150),
inference(clausify,[status(thm)],[f_290_4]) ).
cnf(f_290_6,negated_conjecture,
( well_ordering(sK150)
| well_orders(sK150,relation_field(sK150)) ),
inference(clausify,[status(thm)],[f_290_4]) ).
cnf(f_290_7,negated_conjecture,
( ~ well_orders(sK150,relation_field(sK150))
| well_orders(sK150,relation_field(sK150)) ),
inference(clausify,[status(thm)],[f_290_4]) ).
cnf(f_290_8,negated_conjecture,
( well_ordering(sK150)
| ~ well_ordering(sK150) ),
inference(clausify,[status(thm)],[f_290_4]) ).
cnf(f_290_9,negated_conjecture,
( ~ well_orders(sK150,relation_field(sK150))
| ~ well_ordering(sK150) ),
inference(clausify,[status(thm)],[f_290_4]) ).
fof(f_291_1,plain,
! [A,B,C] :
( subset(set_union2(A,C),B)
| ~ subset(C,B)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t8_xboole_1]) ).
fof(f_291_2,plain,
! [U_1048,U_1047,U_1046] :
( subset(set_union2(U_1048,U_1046),U_1047)
| ~ subset(U_1046,U_1047)
| ~ subset(U_1048,U_1047) ),
inference(variable_rename,[status(thm)],[f_291_1]) ).
cnf(f_291_3,plain,
( subset(set_union2(U_1048,U_1046),U_1047)
| ~ subset(U_1046,U_1047)
| ~ subset(U_1048,U_1047) ),
inference(clausify,[status(thm)],[f_291_2]) ).
fof(f_292_1,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t8_zfmisc_1]) ).
fof(f_292_2,plain,
! [U_1051,U_1050,U_1049] :
( U_1051 = U_1050
| singleton(U_1051) != unordered_pair(U_1050,U_1049) ),
inference(variable_rename,[status(thm)],[f_292_1]) ).
fof(f_292_3,plain,
! [U_1051,U_1050] :
( ! [U_1049] : singleton(U_1051) != unordered_pair(U_1050,U_1049)
| U_1051 = U_1050 ),
inference(miniscope,[status(thm)],[f_292_2]) ).
cnf(f_292_4,plain,
( singleton(U_1051) != unordered_pair(U_1050,U_1049)
| U_1051 = U_1050 ),
inference(clausify,[status(thm)],[f_292_3]) ).
fof(f_293_1,plain,
! [A,B] :
( relation_dom(relation_dom_restriction(B,A)) = set_intersection2(relation_dom(B),A)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t90_relat_1]) ).
fof(f_293_2,plain,
! [U_1053,U_1052] :
( relation_dom(relation_dom_restriction(U_1052,U_1053)) = set_intersection2(relation_dom(U_1052),U_1053)
| ~ relation(U_1052) ),
inference(variable_rename,[status(thm)],[f_293_1]) ).
cnf(f_293_3,plain,
( relation_dom(relation_dom_restriction(U_1052,U_1053)) = set_intersection2(relation_dom(U_1052),U_1053)
| ~ relation(U_1052) ),
inference(clausify,[status(thm)],[f_293_2]) ).
fof(f_294_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t92_zfmisc_1]) ).
fof(f_294_2,plain,
! [U_1055,U_1054] :
( subset(U_1055,union(U_1054))
| ~ in(U_1055,U_1054) ),
inference(variable_rename,[status(thm)],[f_294_1]) ).
cnf(f_294_3,plain,
( subset(U_1055,union(U_1054))
| ~ in(U_1055,U_1054) ),
inference(clausify,[status(thm)],[f_294_2]) ).
fof(f_295_1,plain,
! [A,B] :
( relation_dom_restriction(B,A) = relation_composition(identity_relation(A),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t94_relat_1]) ).
fof(f_295_2,plain,
! [U_1057,U_1056] :
( relation_dom_restriction(U_1056,U_1057) = relation_composition(identity_relation(U_1057),U_1056)
| ~ relation(U_1056) ),
inference(variable_rename,[status(thm)],[f_295_1]) ).
cnf(f_295_3,plain,
( relation_dom_restriction(U_1056,U_1057) = relation_composition(identity_relation(U_1057),U_1056)
| ~ relation(U_1056) ),
inference(clausify,[status(thm)],[f_295_2]) ).
fof(f_296_1,plain,
! [A,B] :
( subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t99_relat_1]) ).
fof(f_296_2,plain,
! [U_1059,U_1058] :
( subset(relation_rng(relation_dom_restriction(U_1058,U_1059)),relation_rng(U_1058))
| ~ relation(U_1058) ),
inference(variable_rename,[status(thm)],[f_296_1]) ).
cnf(f_296_3,plain,
( subset(relation_rng(relation_dom_restriction(U_1058,U_1059)),relation_rng(U_1058))
| ~ relation(U_1058) ),
inference(clausify,[status(thm)],[f_296_2]) ).
fof(f_297_1,plain,
! [A] : union(powerset(A)) = A,
inference(fof_nnf,[status(thm)],[t99_zfmisc_1]) ).
fof(f_297_2,plain,
! [U_1060] : union(powerset(U_1060)) = U_1060,
inference(variable_rename,[status(thm)],[f_297_1]) ).
cnf(f_297_3,plain,
union(powerset(U_1060)) = U_1060,
inference(clausify,[status(thm)],[f_297_2]) ).
fof(f_298_1,plain,
! [A] :
? [B] :
( ! [C] :
( in(C,B)
| are_equipotent(C,B)
| ~ subset(C,B) )
& ! [C] :
( ? [D] :
( ! [E] :
( in(E,D)
| ~ subset(E,C) )
& in(D,B) )
| ~ in(C,B) )
& ! [C,D] :
( in(D,B)
| ~ subset(D,C)
| ~ in(C,B) )
& in(A,B) ),
inference(fof_nnf,[status(thm)],[t9_tarski]) ).
fof(f_298_2,plain,
! [U_1068] :
? [U_1067] :
( ! [U_1066] :
( in(U_1066,U_1067)
| are_equipotent(U_1066,U_1067)
| ~ subset(U_1066,U_1067) )
& ! [U_1065] :
( ? [U_1064] :
( ! [U_1063] :
( in(U_1063,U_1064)
| ~ subset(U_1063,U_1065) )
& in(U_1064,U_1067) )
| ~ in(U_1065,U_1067) )
& ! [U_1062,U_1061] :
( in(U_1061,U_1067)
| ~ subset(U_1061,U_1062)
| ~ in(U_1062,U_1067) )
& in(U_1068,U_1067) ),
inference(variable_rename,[status(thm)],[f_298_1]) ).
fof(f_298_3,plain,
! [U_1068] :
( ! [U_1066] :
( in(U_1066,sK151(U_1068))
| are_equipotent(U_1066,sK151(U_1068))
| ~ subset(U_1066,sK151(U_1068)) )
& ! [U_1065] :
( ? [U_1064] :
( ! [U_1063] :
( in(U_1063,U_1064)
| ~ subset(U_1063,U_1065) )
& in(U_1064,sK151(U_1068)) )
| ~ in(U_1065,sK151(U_1068)) )
& ! [U_1062,U_1061] :
( in(U_1061,sK151(U_1068))
| ~ subset(U_1061,U_1062)
| ~ in(U_1062,sK151(U_1068)) )
& in(U_1068,sK151(U_1068)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK151]),skolemize(U_1067,sK151(U_1068))],[f_298_2]) ).
fof(f_298_4,plain,
! [U_1068] :
( ! [U_1066] :
( in(U_1066,sK151(U_1068))
| are_equipotent(U_1066,sK151(U_1068))
| ~ subset(U_1066,sK151(U_1068)) )
& ! [U_1065] :
( ( ! [U_1063] :
( in(U_1063,sK152(U_1068,U_1065))
| ~ subset(U_1063,U_1065) )
& in(sK152(U_1068,U_1065),sK151(U_1068)) )
| ~ in(U_1065,sK151(U_1068)) )
& ! [U_1062,U_1061] :
( in(U_1061,sK151(U_1068))
| ~ subset(U_1061,U_1062)
| ~ in(U_1062,sK151(U_1068)) )
& in(U_1068,sK151(U_1068)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK152]),skolemize(U_1064,sK152(U_1068,U_1065))],[f_298_3]) ).
cnf(f_298_5,plain,
in(U_1068,sK151(U_1068)),
inference(clausify,[status(thm)],[f_298_4]) ).
cnf(f_298_6,plain,
( in(U_1061,sK151(U_1068))
| ~ subset(U_1061,U_1062)
| ~ in(U_1062,sK151(U_1068)) ),
inference(clausify,[status(thm)],[f_298_4]) ).
cnf(f_298_7,plain,
( in(sK152(U_1068,U_1065),sK151(U_1068))
| ~ in(U_1065,sK151(U_1068)) ),
inference(clausify,[status(thm)],[f_298_4]) ).
cnf(f_298_8,plain,
( in(U_1063,sK152(U_1068,U_1065))
| ~ subset(U_1063,U_1065)
| ~ in(U_1065,sK151(U_1068)) ),
inference(clausify,[status(thm)],[f_298_4]) ).
cnf(f_298_9,plain,
( in(U_1066,sK151(U_1068))
| are_equipotent(U_1066,sK151(U_1068))
| ~ subset(U_1066,sK151(U_1068)) ),
inference(clausify,[status(thm)],[f_298_4]) ).
fof(f_299_1,plain,
! [A,B,C] :
( B = C
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t9_zfmisc_1]) ).
fof(f_299_2,plain,
! [U_1071,U_1070,U_1069] :
( U_1070 = U_1069
| singleton(U_1071) != unordered_pair(U_1070,U_1069) ),
inference(variable_rename,[status(thm)],[f_299_1]) ).
cnf(f_299_3,plain,
( U_1070 = U_1069
| singleton(U_1071) != unordered_pair(U_1070,U_1069) ),
inference(clausify,[status(thm)],[f_299_2]) ).
cnf(f_6_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_3]) ).
cnf(f_6_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_4]) ).
cnf(f_65_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_65_8]) ).
cnf(f_65_9_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_65_9]) ).
cnf(f_69_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_69_2]) ).
cnf(f_70_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_70_2]) ).
cnf(f_71_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_71_2]) ).
cnf(f_72_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_72_2]) ).
cnf(f_73_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_73_2]) ).
cnf(f_74_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_74_2]) ).
cnf(f_75_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_75_2]) ).
cnf(f_76_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_76_2]) ).
cnf(f_77_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_77_2]) ).
cnf(f_78_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_78_2]) ).
cnf(f_80_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_80_2]) ).
cnf(f_82_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_82_2]) ).
cnf(f_83_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_83_2]) ).
cnf(f_84_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_84_2]) ).
cnf(f_85_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_85_2]) ).
cnf(f_87_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_87_2]) ).
cnf(f_88_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_88_2]) ).
cnf(f_90_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_90_2]) ).
cnf(f_91_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_91_2]) ).
cnf(f_100_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_100_2]) ).
cnf(f_101_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_101_2]) ).
cnf(f_290_7_true,negated_conjecture,
$true,
inference(clause_is_true,[status(thm)],[f_290_7]) ).
cnf(f_290_8_true,negated_conjecture,
$true,
inference(clause_is_true,[status(thm)],[f_290_8]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( unordered_pair(Eq_x_0,Eq_x_1) = unordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( set_union2(Eq_x_0,Eq_x_1) = set_union2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( set_intersection2(Eq_x_0,Eq_x_1) = set_intersection2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( identity_relation(Eq_x_0) = identity_relation(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( ordered_pair(Eq_x_0,Eq_x_1) = ordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( relation_dom_restriction(Eq_x_0,Eq_x_1) = relation_dom_restriction(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( relation_image(Eq_x_0,Eq_x_1) = relation_image(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( apply(Eq_x_0,Eq_x_1) = apply(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( relation_rng_restriction(Eq_x_0,Eq_x_1) = relation_rng_restriction(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( relation_field(Eq_x_0) = relation_field(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( relation_inverse_image(Eq_x_0,Eq_x_1) = relation_inverse_image(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( unordered_triple(Eq_x_0,Eq_x_1,Eq_x_2) = unordered_triple(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( succ(Eq_x_0) = succ(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( set_meet(Eq_x_0) = set_meet(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( fiber(Eq_x_0,Eq_x_1) = fiber(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( cartesian_product2(Eq_x_0,Eq_x_1) = cartesian_product2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( cast_to_subset(Eq_x_0) = cast_to_subset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,axiom,
( union(Eq_x_0) = union(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( set_difference(Eq_x_0,Eq_x_1) = set_difference(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,axiom,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_27,axiom,
( subset_complement(Eq_x_0,Eq_x_1) = subset_complement(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,axiom,
( relation_inverse(Eq_x_0) = relation_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_29,axiom,
( relation_composition(Eq_x_0,Eq_x_1) = relation_composition(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_30,axiom,
( complements_of_subsets(Eq_x_0,Eq_x_1) = complements_of_subsets(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_31,axiom,
( function_inverse(Eq_x_0) = function_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_32,axiom,
( union_of_subsets(Eq_x_0,Eq_x_1) = union_of_subsets(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,axiom,
( meet_of_subsets(Eq_x_0,Eq_x_1) = meet_of_subsets(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_34,axiom,
( subset_difference(Eq_x_0,Eq_x_1,Eq_x_2) = subset_difference(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_35,axiom,
( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_36,axiom,
( sK2(Eq_x_0,Eq_x_1) = sK2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_37,axiom,
( sK3(Eq_x_0,Eq_x_1) = sK3(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_38,axiom,
( sK4(Eq_x_0,Eq_x_1) = sK4(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,axiom,
( sK5(Eq_x_0,Eq_x_1,Eq_x_2) = sK5(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_40,axiom,
( sK6(Eq_x_0,Eq_x_1,Eq_x_2) = sK6(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_41,axiom,
( sK7(Eq_x_0,Eq_x_1,Eq_x_2) = sK7(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_42,axiom,
( sK8(Eq_x_0,Eq_x_1,Eq_x_2) = sK8(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_43,axiom,
( sK9(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK9(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_44,axiom,
( sK10(Eq_x_0,Eq_x_1,Eq_x_2) = sK10(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_45,axiom,
( sK11(Eq_x_0,Eq_x_1,Eq_x_2) = sK11(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_46,axiom,
( sK12(Eq_x_0,Eq_x_1,Eq_x_2) = sK12(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_47,axiom,
( sK13(Eq_x_0,Eq_x_1,Eq_x_2) = sK13(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_48,axiom,
( sK14(Eq_x_0,Eq_x_1,Eq_x_2) = sK14(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_49,axiom,
( sK15(Eq_x_0,Eq_x_1,Eq_x_2) = sK15(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_50,axiom,
( sK16(Eq_x_0,Eq_x_1,Eq_x_2) = sK16(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_51,axiom,
( sK17(Eq_x_0,Eq_x_1,Eq_x_2) = sK17(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_52,axiom,
( sK18(Eq_x_0,Eq_x_1,Eq_x_2) = sK18(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_53,axiom,
( sK19(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK19(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_54,axiom,
( sK20(Eq_x_0,Eq_x_1,Eq_x_2) = sK20(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_55,axiom,
( sK21(Eq_x_0,Eq_x_1,Eq_x_2) = sK21(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_56,axiom,
( sK22(Eq_x_0,Eq_x_1,Eq_x_2) = sK22(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_57,axiom,
( sK23(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK23(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_58,axiom,
( sK24(Eq_x_0,Eq_x_1,Eq_x_2) = sK24(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_59,axiom,
( sK25(Eq_x_0,Eq_x_1,Eq_x_2) = sK25(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_60,axiom,
( sK26(Eq_x_0,Eq_x_1,Eq_x_2) = sK26(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_61,axiom,
( sK27(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK27(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_62,axiom,
( sK28(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK28(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_63,axiom,
( sK29(Eq_x_0,Eq_x_1) = sK29(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_64,axiom,
( sK30(Eq_x_0,Eq_x_1) = sK30(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_65,axiom,
( sK31(Eq_x_0) = sK31(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_66,axiom,
( sK32(Eq_x_0,Eq_x_1) = sK32(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_67,axiom,
( sK33(Eq_x_0,Eq_x_1,Eq_x_2) = sK33(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_68,axiom,
( sK34(Eq_x_0,Eq_x_1) = sK34(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_69,axiom,
( sK35(Eq_x_0,Eq_x_1) = sK35(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_70,axiom,
( sK36(Eq_x_0,Eq_x_1) = sK36(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_71,axiom,
( sK37(Eq_x_0,Eq_x_1) = sK37(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_72,axiom,
( sK38(Eq_x_0,Eq_x_1) = sK38(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_73,axiom,
( sK39(Eq_x_0) = sK39(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_74,axiom,
( sK40(Eq_x_0,Eq_x_1) = sK40(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_75,axiom,
( sK41(Eq_x_0,Eq_x_1) = sK41(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_76,axiom,
( sK42(Eq_x_0) = sK42(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_77,axiom,
( sK43(Eq_x_0,Eq_x_1) = sK43(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_78,axiom,
( sK44(Eq_x_0,Eq_x_1) = sK44(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_79,axiom,
( sK45(Eq_x_0,Eq_x_1) = sK45(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_80,axiom,
( sK46(Eq_x_0,Eq_x_1) = sK46(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_81,axiom,
( sK47(Eq_x_0,Eq_x_1,Eq_x_2) = sK47(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_82,axiom,
( sK48(Eq_x_0,Eq_x_1,Eq_x_2) = sK48(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_83,axiom,
( sK49(Eq_x_0,Eq_x_1) = sK49(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_84,axiom,
( sK50(Eq_x_0) = sK50(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_85,axiom,
( sK51(Eq_x_0,Eq_x_1,Eq_x_2) = sK51(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_86,axiom,
( sK52(Eq_x_0,Eq_x_1,Eq_x_2) = sK52(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_87,axiom,
( sK53(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK53(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_88,axiom,
( sK54(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK54(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_89,axiom,
( sK55(Eq_x_0,Eq_x_1,Eq_x_2) = sK55(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_90,axiom,
( sK56(Eq_x_0,Eq_x_1,Eq_x_2) = sK56(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_91,axiom,
( sK57(Eq_x_0,Eq_x_1,Eq_x_2) = sK57(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_92,axiom,
( sK58(Eq_x_0,Eq_x_1,Eq_x_2) = sK58(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_93,axiom,
( sK59(Eq_x_0) = sK59(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_94,axiom,
( sK60(Eq_x_0) = sK60(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_95,axiom,
( sK61(Eq_x_0,Eq_x_1) = sK61(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_96,axiom,
( sK62(Eq_x_0,Eq_x_1) = sK62(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_97,axiom,
( sK63(Eq_x_0,Eq_x_1) = sK63(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_98,axiom,
( sK64(Eq_x_0,Eq_x_1,Eq_x_2) = sK64(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_99,axiom,
( sK65(Eq_x_0,Eq_x_1) = sK65(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_100,axiom,
( sK66(Eq_x_0,Eq_x_1,Eq_x_2) = sK66(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_101,axiom,
( sK67(Eq_x_0,Eq_x_1,Eq_x_2) = sK67(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_102,axiom,
( sK68(Eq_x_0,Eq_x_1,Eq_x_2) = sK68(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_103,axiom,
( sK69(Eq_x_0,Eq_x_1) = sK69(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_104,axiom,
( sK70(Eq_x_0,Eq_x_1) = sK70(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_105,axiom,
( sK71(Eq_x_0,Eq_x_1) = sK71(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_106,axiom,
( sK72(Eq_x_0,Eq_x_1) = sK72(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_107,axiom,
( sK73(Eq_x_0,Eq_x_1) = sK73(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_108,axiom,
( sK74(Eq_x_0,Eq_x_1,Eq_x_2) = sK74(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_109,axiom,
( sK75(Eq_x_0,Eq_x_1) = sK75(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_110,axiom,
( sK76(Eq_x_0,Eq_x_1) = sK76(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_111,axiom,
( sK77(Eq_x_0,Eq_x_1) = sK77(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_112,axiom,
( sK78(Eq_x_0,Eq_x_1,Eq_x_2) = sK78(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_113,axiom,
( sK79(Eq_x_0,Eq_x_1,Eq_x_2) = sK79(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_114,axiom,
( sK80(Eq_x_0,Eq_x_1,Eq_x_2) = sK80(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_115,axiom,
( sK81(Eq_x_0,Eq_x_1) = sK81(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_116,axiom,
( sK82(Eq_x_0,Eq_x_1) = sK82(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_117,axiom,
( sK83(Eq_x_0,Eq_x_1) = sK83(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_118,axiom,
( sK84(Eq_x_0,Eq_x_1,Eq_x_2) = sK84(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_119,axiom,
( sK85(Eq_x_0,Eq_x_1) = sK85(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_120,axiom,
( sK86(Eq_x_0,Eq_x_1) = sK86(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_121,axiom,
( sK87(Eq_x_0,Eq_x_1) = sK87(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_122,axiom,
( sK88(Eq_x_0,Eq_x_1) = sK88(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_123,axiom,
( sK89(Eq_x_0,Eq_x_1) = sK89(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_124,axiom,
( sK90(Eq_x_0,Eq_x_1) = sK90(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_125,axiom,
( sK91(Eq_x_0,Eq_x_1) = sK91(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_126,axiom,
( sK92(Eq_x_0,Eq_x_1) = sK92(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_127,axiom,
( sK93(Eq_x_0,Eq_x_1) = sK93(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_128,axiom,
( sK94(Eq_x_0) = sK94(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_129,axiom,
( sK95(Eq_x_0) = sK95(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_130,axiom,
( sK96(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK96(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_131,axiom,
( sK97(Eq_x_0,Eq_x_1,Eq_x_2) = sK97(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_132,axiom,
( sK98(Eq_x_0,Eq_x_1,Eq_x_2) = sK98(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_133,axiom,
( sK99(Eq_x_0,Eq_x_1,Eq_x_2) = sK99(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_134,axiom,
( sK100(Eq_x_0,Eq_x_1,Eq_x_2) = sK100(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_135,axiom,
( sK101(Eq_x_0,Eq_x_1,Eq_x_2) = sK101(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_136,axiom,
( sK102(Eq_x_0,Eq_x_1) = sK102(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_137,axiom,
( sK103(Eq_x_0,Eq_x_1) = sK103(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_138,axiom,
( sK104(Eq_x_0,Eq_x_1) = sK104(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_139,axiom,
( sK105(Eq_x_0,Eq_x_1,Eq_x_2) = sK105(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_140,axiom,
( sK106(Eq_x_0) = sK106(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_141,axiom,
( sK107(Eq_x_0) = sK107(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_142,axiom,
( sK108(Eq_x_0) = sK108(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_143,axiom,
( sK109(Eq_x_0) = sK109(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_144,axiom,
( sK110(Eq_x_0) = sK110(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_145,axiom,
( sK111(Eq_x_0) = sK111(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_146,axiom,
( sK112(Eq_x_0) = sK112(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_147,axiom,
( sK113(Eq_x_0) = sK113(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_148,axiom,
( sK114(Eq_x_0) = sK114(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_149,axiom,
( sK115(Eq_x_0,Eq_x_1) = sK115(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_150,axiom,
( sK119(Eq_x_0) = sK119(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_151,axiom,
( sK124(Eq_x_0) = sK124(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_152,axiom,
( sK130(Eq_x_0) = sK130(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_153,axiom,
( sK131(Eq_x_0,Eq_x_1,Eq_x_2) = sK131(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_154,axiom,
( sK132(Eq_x_0,Eq_x_1,Eq_x_2) = sK132(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_155,axiom,
( sK133(Eq_x_0,Eq_x_1) = sK133(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_156,axiom,
( sK134(Eq_x_0,Eq_x_1) = sK134(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_157,axiom,
( sK135(Eq_x_0) = sK135(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_158,axiom,
( sK136(Eq_x_0,Eq_x_1) = sK136(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_159,axiom,
( sK137(Eq_x_0,Eq_x_1) = sK137(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_160,axiom,
( sK138(Eq_x_0,Eq_x_1) = sK138(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_161,axiom,
( sK139(Eq_x_0) = sK139(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_162,axiom,
( sK140(Eq_x_0) = sK140(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_163,axiom,
( sK141(Eq_x_0,Eq_x_1) = sK141(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_164,axiom,
( sK142(Eq_x_0,Eq_x_1) = sK142(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_165,axiom,
( sK143(Eq_x_0,Eq_x_1) = sK143(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_166,axiom,
( sK144(Eq_x_0,Eq_x_1) = sK144(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_167,axiom,
( sK145(Eq_x_0,Eq_x_1) = sK145(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_168,axiom,
( sK146(Eq_x_0) = sK146(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_169,axiom,
( sK147(Eq_x_0) = sK147(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_170,axiom,
( sK148(Eq_x_0,Eq_x_1,Eq_x_2) = sK148(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_171,axiom,
( sK149(Eq_x_0,Eq_x_1) = sK149(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_172,axiom,
( sK151(Eq_x_0) = sK151(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_173,axiom,
( sK152(Eq_x_0,Eq_x_1) = sK152(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_174,axiom,
( in(Eq_y_0,Eq_y_1)
| ~ in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_175,axiom,
( proper_subset(Eq_y_0,Eq_y_1)
| ~ proper_subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_176,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_177,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_178,axiom,
( ordinal(Eq_y_0)
| ~ ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_179,axiom,
( epsilon_transitive(Eq_y_0)
| ~ epsilon_transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_180,axiom,
( epsilon_connected(Eq_y_0)
| ~ epsilon_connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_181,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_182,axiom,
( one_to_one(Eq_y_0)
| ~ one_to_one(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_183,axiom,
( ordinal_subset(Eq_y_0,Eq_y_1)
| ~ ordinal_subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_184,axiom,
( subset(Eq_y_0,Eq_y_1)
| ~ subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_185,axiom,
( antisymmetric(Eq_y_0)
| ~ antisymmetric(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_186,axiom,
( is_antisymmetric_in(Eq_y_0,Eq_y_1)
| ~ is_antisymmetric_in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_187,axiom,
( connected(Eq_y_0)
| ~ connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_188,axiom,
( is_connected_in(Eq_y_0,Eq_y_1)
| ~ is_connected_in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_189,axiom,
( transitive(Eq_y_0)
| ~ transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_190,axiom,
( is_transitive_in(Eq_y_0,Eq_y_1)
| ~ is_transitive_in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_191,axiom,
( is_reflexive_in(Eq_y_0,Eq_y_1)
| ~ is_reflexive_in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_192,axiom,
( element(Eq_y_0,Eq_y_1)
| ~ element(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_193,axiom,
( well_founded_relation(Eq_y_0)
| ~ well_founded_relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_194,axiom,
( disjoint(Eq_y_0,Eq_y_1)
| ~ disjoint(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_195,axiom,
( is_well_founded_in(Eq_y_0,Eq_y_1)
| ~ is_well_founded_in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_196,axiom,
( well_ordering(Eq_y_0)
| ~ well_ordering(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_197,axiom,
( reflexive(Eq_y_0)
| ~ reflexive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_198,axiom,
( well_orders(Eq_y_0,Eq_y_1)
| ~ well_orders(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_199,axiom,
( being_limit_ordinal(Eq_y_0)
| ~ being_limit_ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_200,axiom,
( relation_empty_yielding(Eq_y_0)
| ~ relation_empty_yielding(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_201,axiom,
( are_equipotent(Eq_y_0,Eq_y_1)
| ~ are_equipotent(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU244+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 23:44:05 UTC 2026
% 0.10/0.36 % CPUTime :
% 77.36/77.68 % SZS status Theorem for theBenchmark
% 77.36/77.68 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------